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0000fb021000070000000000bc02000000000102022253797374656d0006040000002d01010004000000f0010200030000000000ffffffffffffffffffffffffffffffffffffffffffff}{\result {\f0\fs24\dn38\insrsid8198892 
{\pict{\*\picprop\shplid1028{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}
\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw2505\pich1588\picwgoal1420\pichgoal900\wmetafile8\bliptag1973362282\blipupi-611{\*\blipuid 759f1e6af78a96f4d1eb151ce74c8b7d}
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\par }\pard \qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\f0\fs24\ul\insrsid8198892 
\par }{\f0\fs24\insrsid8198892 Donde  }{\b\f0\fs24\insrsid8198892 u }{\f0\fs24\insrsid8198892 lo hemos derivado y }{\b\f0\fs24\insrsid8198892 dv}{\f0\fs24\insrsid8198892  lo hemos integrado.
\par Aplicando la f\'f3rmula que hemos indicado anteriormente,  }{\pard\plain \qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \fs24\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\object\objemb\objw2680\objh620
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7374656d0000040000002d01020004000000f0010100030000000000}{\result {\f0\fs24\dn24\insrsid8198892 {\pict{\*\picprop\shplid1029{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}
{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw4727\pich1094\picwgoal2680\pichgoal620\wmetafile8\bliptag-1584481432\blipupi254{\*\blipuid a18ebb68d117dce0640eecf71df188df}
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\par La integral resultante es de tipo logar\'edtmico: 
\par 
\par }{\pard\plain \qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \fs24\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\object\objemb\objw4981\objh620{\*\objclass Equation.3}{\*\objdata 01050000020000000b000000
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{\pict{\*\picprop\shplid1030{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}
{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw8784\pich1094\picwgoal4980\pichgoal620\wmetafile8\bliptag1887610677\blipupi-111{\*\blipuid 7082a7350b2fac8a48fcc02ef08edb82}
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\f0\fs24\insrsid8198892 +C
\par 
\par 
\par }\pard \ql \li0\ri0\widctlpar\brdrt\brdrs\brdrw15\brsp20 \brdrl\brdrs\brdrw15\brsp20 \brdrb\brdrs\brdrw15\brsp20 \brdrr\brdrs\brdrw15\brsp20 \aspalpha\aspnum\faauto\adjustright\rin0\lin0\rtlgutter\itap0 \shading2500\cbpat8 {\f0\fs24\insrsid8198892  }{
\b\f0\fs24\insrsid8198892 b)        I=}{\pard\plain \ql \li0\ri0\widctlpar\brdrt\brdrs\brdrw15\brsp20 \brdrl\brdrs\brdrw15\brsp20 \brdrb\brdrs\brdrw15\brsp20 \brdrr\brdrs\brdrw15\brsp20 \aspalpha\aspnum\faauto\adjustright\rin0\lin0\rtlgutter\itap0 
\b\fs24\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\object\objemb\objw1240\objh560{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e3300000000000000000060000000
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00009001000000000402001054696d6573204e657720526f6d616e000081040000002d01010004000000f001000008000000320a74015d020100000032000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01000004000000
f0010100030000000000}{\result {\b\f0\fs24\dn22\insrsid8198892 {\pict{\*\picprop\shplid1031{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}
{\sp{\sn fillColor}{\sv 12632256}}{\sp{\sn fFilled}{\sv 1}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}
\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw2187\pich988\picwgoal1240\pichgoal560\wmetafile8\bliptag-1245485865\blipupi-1454{\*\blipuid b5c364d7962c2bbefbae4458152fc4d0}
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\par }\pard \ql \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\f0\fs24\ul\insrsid8198892 
\par Soluci\'f3n:  
\par }\pard \ql \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\pard\plain \ql \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \fs24\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\object\objemb
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{\pict{\*\picprop\shplid1032{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}
{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw2397\pich1341\picwgoal1359\pichgoal760\wmetafile8\bliptag-631639841\blipupi-886{\*\blipuid da59f0df994615da75669dbefef40370}
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\ql \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \fs24\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\object\objemb\objw2220\objh880{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e330000000000
0000000080000000
02010101000a0401010112836412837502863d028832128378128364128378000112837602863d031502000112827312826512826e12837812836412837802863d02862d12826312826f128273128378000b010001000d0286f200000000c00000000000000000000000000000000000000000000000000000000000ff00
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01000000780009000000320a3804fc05030000007864780008000000320a3804340001000000760009000000320a51012404030000007864780008000000320a51013a0002000000647515000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000081040000002d0101000400
0000f001000009000000320a38049a0a03000000636f730009000000320a3804aa030300000073656e0008000000320a51014c030100000032000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01000004000000f0010100
030000000000}{\result {\f0\fs24\dn38\insrsid8198892 {\pict{\*\picprop\shplid1033{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}
{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}
\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw3916\pich1552\picwgoal2220\pichgoal880\wmetafile8\bliptag-1563696402\blipupi122{\*\blipuid a2cbe2ee22c848470690b559c65904d0}
0100090000033e0100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c028005e00d1200000026060f001a00ffffffff000010000000c0ffffffd5ffffffa00d0000550500000b00000026060f00
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01000000f20010000000fb0280fe0000000000009001000000020002001053796d626f6c0002040000002d01010004000000f001000008000000320a38049809
010000002d0008000000320a38046c08010000003d0008000000320a38043c01010000003d0008000000320a51012002010000003d0015000000fb0280fe0000
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0000647515000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000081040000002d01010004000000f00100000900
0000320a38049a0a03000000636f730009000000320a3804aa030300000073656e0008000000320a51014c030100000032000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01000004000000f0010100030000000000}}}}}{
\f0\fs24\insrsid8198892 
\par }\pard \ql \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\f0\fs24\insrsid8198892 I=}{\pard\plain \ql \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \fs24\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 
{\object\objemb\objw2360\objh560{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e3300000000000000000080000000
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000001050000050000000d0000004d45544146494c4550494354004310000024fcffffaa02000008004310dc030000
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0f000c004d617468547970650000b00015000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d616e000081040000002d01000008000000320a20021e0d02000000647808000000320a2002820c01000000780008000000320a20025e0901000000780008000000320a20022e050100
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0000f001010008000000320a20021e06010000002b0008000000320a20023a00010000002d0015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000081040000002d01010004000000f001000009000000320a20023c0a03000000636f730008000000320a200286080100
0000320009000000320a2002e80203000000636f730015000000fb0220ff0000000000009001000000000402001054696d6573204e657720526f6d616e000081040000002d01000004000000f001010008000000320a740123020100000032000a00000026060f000a00ffffffff01000000000010000000fb0210000700
00000000bc02000000000102022253797374656d0000040000002d01010004000000f0010000030000000000}{\result {\f0\fs24\dn22\insrsid8198892 {\pict{\*\picprop\shplid1034{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}
{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw4163\pich988\picwgoal2360\pichgoal560\wmetafile8\bliptag-604000500\blipupi-12{\*\blipuid dbffaf0cc4fad7e05b773dcabb4a69d7}010009000003510100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c028003c00e1200000026060f001a00ffffffff000010000000c0ffffffadffffff800e00002d0300000b00000026060f00
0c004d617468547970650000b00015000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d616e000081040000002d010000
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08000000320a20021e06010000002b0008000000320a20023a00010000002d0015000000fb0280fe0000000000009001000000000402001054696d6573204e65
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320a2002e80203000000636f730015000000fb0220ff0000000000009001000000000402001054696d6573204e657720526f6d616e000081040000002d010000
04000000f001010008000000320a740123020100000032000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01010004000000f0010000030000000000}}}}}{\f0\fs24\insrsid8198892 
.   (*)   A  veces hay que repetir la in\-tegraci\'f3n por partes como en este caso:  
\par 
\par }{\pard\plain \ql \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \fs24\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\object\objemb\objw1359\objh720{\*\objclass Equation.3}{\*\objdata 01050000020000000b000000
4571756174696f6e2e330000000000000000006000000002010101000a01030202000401010112837502863d028832128378000112836412837602863d12826312826f128273128378128364128378000002967d00000000000000000000000000000000000000000000000000000000000000000000000105000005000000
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010009000003140100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c02800480081200000026060f001a00ffffffff000010000000c0ffffffc0ffffff40080000400400000b0000002606
0f000c004d617468547970650000f00010000000fb0280fe0000000000009001000000020002001053796d626f6c0002040000002d01000008000000320a2204900701000000fe0008000000320ae202900701000000fd0008000000320aa201900701000000fc0008000000320ac6030202010000003d0008000000320a
86015401010000003d0015000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d616e000081040000002d01010004000000f001000009000000320ac6036e05030000007864780008000000320ac6033a0002000000647608000000320a8601580301000000780008000000320a8601
2e0001000000750015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000081040000002d01000004000000f001010009000000320ac603280303000000636f730008000000320a860180020100000032000a00000026060f000a00ffffffff01000000000010000000fb02
1000070000000000bc02000000000102022253797374656d0000040000002d01010004000000f0010000030000000000}{\result {\f0\fs24\dn30\insrsid8198892 {\pict{\*\picprop\shplid1035{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}
{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw2397\pich1270\picwgoal1359\pichgoal720\wmetafile8\bliptag1722663925\blipupi-948{\*\blipuid 66adc3f5cf18e7c710ae599d05cd2976}
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0c004d617468547970650000f00010000000fb0280fe0000000000009001000000020002001053796d626f6c0002040000002d01000008000000320a22049007
01000000fe0008000000320ae202900701000000fd0008000000320aa201900701000000fc0008000000320ac6030202010000003d0008000000320a86015401
010000003d0015000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d616e000081040000002d01010004000000f0010000
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750015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000081040000002d01000004000000f001010009000000
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{\pard\plain \ql \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \fs24\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\object\objemb\objw1981\objh800{\*\objclass Equation.3}{\*\objdata 01050000020000000b000000
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030000007864780008000000320af403340001000000760008000000320a5a01120402000000647808000000320a5a013a0002000000647515000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000081040000002d01010004000000f001000009000000320af40319090300
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\f0\fs24\dn34\insrsid8198892 {\pict{\*\picprop\shplid1036{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}
{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}
\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw3493\pich1411\picwgoal1980\pichgoal800\wmetafile8\bliptag1289949478\blipupi-129{\*\blipuid 4ce3112611fe97f6d6e41ffaafda577c}
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050000000b0200000000050000000c020005600c1200000026060f001a00ffffffff000010000000c0ffffffccffffff200c0000cc0400000b00000026060f00
0c004d617468547970650000100110000000fb02c0fd0000000000009001000000020002001053796d626f6c0002040000002d01000008000000320a7e046e02
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780008000000320af403340001000000760008000000320a5a01120402000000647808000000320a5a013a0002000000647515000000fb0280fe000000000000
9001000000000402001054696d6573204e657720526f6d616e000081040000002d01010004000000f001000009000000320af40319090300000073656e000900
0000320af403430303000000636f730008000000320a5a014c030100000032000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01000004000000f0010100030000000000}}}}}{\f0\fs24\insrsid8198892 
\par }{\pard\plain \ql \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \fs24\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\object\objemb\objw5360\objh560{\*\objclass Equation.3}{\*\objdata 01050000020000000b000000
4571756174696f6e2e33000000000000000000c0000000
02010101000a01031502000102883212837812826312826f12827312837812836412837802863d02883212837812827312826512826e12837802862d031502000102883212827312826512826e12837812836412837802863d02883212837812827312826512826e12837802862b02883212826312826f12827312837800
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0f000c004d617468547970650000b00010000000fb02c0fd0000000000009001000000020002001053796d626f6c0002040000002d01000008000000320aaa02400001000000f20008000000320aaa022c0f01000000f20010000000fb0280fe0000000000009001000000020002001053796d626f6c0002040000002d01
010004000000f001000008000000320a2002381c010000002b0008000000320a20021a16010000003d0008000000320a2002120e010000002d0008000000320a2002f407010000003d0015000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d616e000081040000002d0100000400
0000f001010008000000320a2002822001000000780008000000320a2002481b01000000780008000000320a20021e1801000000780009000000320a2002aa13030000007864780008000000320a2002220d01000000780008000000320a2002f80901000000780009000000320a20028405030000007864780008000000
320a2002600201000000780015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000081040000002d01010004000000f001000009000000320a20023c1e03000000636f730008000000320a2002521d01000000320009000000320a2002f6180300000073656e0008000000
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ffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01000004000000f0010100030000000000}{\result {\f0\fs24\dn22\insrsid8198892 {\pict{\*\picprop\shplid1037{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}
{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw9454\pich988\picwgoal5360\pichgoal560\wmetafile8\bliptag-1559616326\blipupi18{\*\blipuid a30a24baac5340b10973da8f14533f79}010009000003990100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c02800380211200000026060f001a00ffffffff000010000000c0ffffffadffffff402100002d0300000b00000026060f00
0c004d617468547970650000b00010000000fb02c0fd0000000000009001000000020002001053796d626f6c0002040000002d01000008000000320aaa024000
01000000f20008000000320aaa022c0f01000000f20010000000fb0280fe0000000000009001000000020002001053796d626f6c0002040000002d0101000400
0000f001000008000000320a2002381c010000002b0008000000320a20021a16010000003d0008000000320a2002120e010000002d0008000000320a2002f407
010000003d0015000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d616e000081040000002d01000004000000f0010100
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780008000000320a2002220d01000000780008000000320a2002f80901000000780009000000320a20028405030000007864780008000000320a200260020100
0000780015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000081040000002d01010004000000f00100000900
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320009000000320a200258110300000073656e0008000000320a2002741001000000320009000000320a2002d00a0300000073656e0008000000320a20022009
01000000320009000000320a20023e0303000000636f730008000000320a200288010100000032000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01000004000000f0010100030000000000}}}}}{
\f0\fs24\insrsid8198892 
\par }\pard \qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\f0\fs24\insrsid8198892 Y volviendo a la expresi\'f3n (*) obtenemos el resultado final:
\par }\pard \qj \li2124\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin2124\itap0 {\f0\fs24\insrsid8198892  }{\pard\plain \qj \li2124\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin2124\itap0 
\fs24\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\object\objemb\objw3240\objh420{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e3300000000000000000080000000
02010101000a0112834902863d02862d128378030f02000b01000102883200000a12826312826f12827312837802862b02883212837812827312826512826e12837802862b02883212826312826f1282731283780000ef6ffe27f272fe27ef6f000000000000000000000000000000000000000000000000000000000000
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0100030000000000}{\result {\f0\fs24\dn14\insrsid8198892 {\pict{\*\picprop\shplid1038{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}
{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw5715\pich741\picwgoal3240\pichgoal420\wmetafile8\bliptag76277229\blipupi456{\*\blipuid 048be5ed3c947f1475e82f1bd6bddc5b}
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\f0\fs24\insrsid8198892 +C
\par }\pard \ql \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\b\i\f36\fs24\ul\insrsid8198892 
\par 
\par }{\b\i\f1\ul\insrsid8198892 
\par 
\par METODO DE SUSTITUCION O CAMBIO DE VARIABLE.
\par }\pard \qj \li0\ri0\widctlpar\tx2835\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\i\f1\insrsid8198892 Consiste en sustituir la variable x por otra variable t mediante una nueva funci\'f3
n g tal que x=g(t)  a fin de transformar el integrando en otro m\'e1s sencillo}{\f1\insrsid8198892 .
\par }\pard \qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\b\f0\fs24\ul\insrsid8198892 
\par Ejemplos:
\par 
\par }\pard \qj \li0\ri0\widctlpar\brdrt\brdrs\brdrw15\brsp20 \brdrl\brdrs\brdrw15\brsp20 \brdrb\brdrs\brdrw15\brsp20 \brdrr\brdrs\brdrw15\brsp20 \aspalpha\aspnum\faauto\adjustright\rin0\lin0\rtlgutter\itap0 \shading2500\cbpat8 {\b\f0\fs24\insrsid8198892 a)}{
\f0\fs24\insrsid8198892  }{\pard\plain \qj \li0\ri0\widctlpar\brdrt\brdrs\brdrw15\brsp20 \brdrl\brdrs\brdrw15\brsp20 \brdrb\brdrs\brdrw15\brsp20 \brdrr\brdrs\brdrw15\brsp20 \aspalpha\aspnum\faauto\adjustright\rin0\lin0\rtlgutter\itap0 
\fs24\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\object\objemb\objw1300\objh639{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e3300000000000000000080000000
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ffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01020004000000f0010300030000000000}{\result {\b\f0\fs24\dn26\insrsid8198892 {\pict{\*\picprop\shplid1039{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fillColor}{\sv 12632256}}{\sp{\sn fFilled}{\sv 1}}{\sp{\sn fHitTestFill}{\sv 1}}
{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw2293\pich1127\picwgoal1300\pichgoal639\wmetafile8\bliptag1347086205\blipupi-1182{\*\blipuid 504ae77d80df0341c47d238acbc0c8a1}
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\f0\fs24\insrsid8198892 
\par }\pard \qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\f0\fs24\ul\insrsid8198892 
\par }\pard \qj \li0\ri0\sl360\slmult1\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\f0\fs24\ul\insrsid8198892 Soluci\'f3n:
\par }{\f0\fs24\insrsid8198892 Hacemos el cambio }{\pard\plain \qj \li0\ri0\sl360\slmult1\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \fs24\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\object\objemb\objw1000\objh300
{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e3300000000000000000060000000
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070000002105010031000000000010000000fb021000070000000000bc02000000000102022253797374656d0006040000002d01030004000000f0010200030000000000}{\result {\f0\fs24\dn4\insrsid8198892 {\pict{\*\picprop\shplid1040{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw1764\pich529\picwgoal1000\pichgoal300\wmetafile8\bliptag192511570\blipupi2305{\*\blipuid 0b797e52fc68f270a6aedea44a54b997}0100090000031e0100000400150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01190005000000310201000000
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\f0\fs24\insrsid8198892   y elevando al cuadrado, x-1 = t}{\f0\fs24\up6\insrsid8198892 2}{\f0\fs24\insrsid8198892 
\par Diferenciando la igualdad anterior, dx = 2t.dt
\par Por otra parte, de x-1 = t}{\f0\fs24\up6\insrsid8198892 2}{\f0\fs24\insrsid8198892  resulta x = 1+t}{\f0\fs24\up6\insrsid8198892 2}{\f0\fs24\insrsid8198892 
\par Sustituyendo resulta:
\par }\pard \qj \li708\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin708\itap0 {\pard\plain \qj \li708\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin708\itap0 \fs24\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\object\objemb
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656d0000040000002d01030004000000f0010200030000000000}{\result {\f0\fs24\dn32\insrsid8198892 {\pict{\*\picprop\shplid1041{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}
{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw7973\pich1235\picwgoal4520\pichgoal700\wmetafile8\bliptag-784590278\blipupi-287{\*\blipuid d13c1a3afd6308b0a4f86dc9545d11de}
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\par }\pard \qj \li708\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin708\itap0 {\pard\plain \qj \li708\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin708\itap0 \fs24\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\object\objemb
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\par 
\par 
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\f0\fs24\insrsid8198892   }{\pard\plain \qj \li0\ri0\widctlpar\brdrt\brdrs\brdrw15\brsp20 \brdrl\brdrs\brdrw15\brsp20 \brdrb\brdrs\brdrw15\brsp20 \brdrr\brdrs\brdrw15\brsp20 \aspalpha\aspnum\faauto\adjustright\rin0\lin0\rtlgutter\itap0 
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\par }\pard \qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\f0\fs24\ul\insrsid8198892 
\par Soluci\'f3n:
\par }{\f0\fs24\insrsid8198892 Hacemos el cambio  }{\pard\plain \qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \fs24\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\object\objemb\objw3120\objh420{\*\objclass Equation.3}
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\par Sustituyendo en la integral resulta:
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{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw4798\pich1411\picwgoal2720\pichgoal800\wmetafile8\bliptag529777633\blipupi382{\*\blipuid 1f93c3e182d82e714b7d49fe739d1254}
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\par }\pard \qj \li708\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin708\itap0 {\f0\fs24\insrsid8198892 
\par 
\par 
\par 
\par 
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\par }\pard \qj \li0\ri0\sl360\slmult1\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\f0\fs24\ul\insrsid8198892 Soluci\'f3n:
\par }{\f0\fs24\insrsid8198892 El cambio que podemos realizar es el siguiente: senx=t   (Por ser impar en cosx)
\par De dicho cambio resulta: cosxdx=dt y sustituyendo en la integral pro\-puesta obtenemos:
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\par 
\par }\pard \qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\f0\fs24\insrsid8198892 
\par }\pard \ql \li0\ri0\widctlpar\brdrt\brdrs\brdrw15\brsp20 \brdrl\brdrs\brdrw15\brsp20 \brdrb\brdrs\brdrw15\brsp20 \brdrr\brdrs\brdrw15\brsp20 \aspalpha\aspnum\faauto\adjustright\rin0\lin0\rtlgutter\itap0 \shading2500\cbpat8 {\b\f0\fs24\insrsid8198892 e)}{
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{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}
\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw9560\pich1341\picwgoal5420\pichgoal760\wmetafile8\bliptag1275505660\blipupi115{\*\blipuid 4c06abfcf8565b4ba9f86a7d66f926dd}
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\f0\fs24\insrsid8198892 
\par }\pard \qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\b\i\f0\fs24\ul\insrsid8198892 
\par 
\par }\pard\plain \s4\qj \li0\ri0\keepn\widctlpar\aspalpha\aspnum\faauto\outlinelevel3\adjustright\rin0\lin0\itap0 \b\f1\fs20\ul\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\insrsid8198892 METODO DE DESCOMPOSICION EN FRACCIONES SIMPLES
\par }\pard\plain \s17\qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \b\f38\fs28\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\b0\f1\fs20\insrsid8198892 Suponemos que el grado del numerador es menor que el grado del de\-
nominador , pues en caso contrario, se hace la divisi\'f3n y despu\'e9s se integra el cociente m\'e1s el resto partido por el divisor, es decir}{\insrsid8198892 ,
\par }\pard\plain \qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \f37\fs20\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\pard\plain \qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 
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{\pict{\*\picprop\shplid1057{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}
{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw1834\pich1164\picwgoal1040\pichgoal660\wmetafile8\bliptag126408743\blipupi-1675{\*\blipuid 0788d827a4726a0837f243ed14f23977}
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0a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01020004000000f0010100030000000000}}}}}{\b\f0\fs24\insrsid8198892  }{\f0\fs24\insrsid8198892 donde el grado de p(x) es igual o mayor que el de q(x), en\-
tonces}{\b\f0\fs24\insrsid8198892 ,     
\par }{\f0\fs24\insrsid8198892 
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\f0\fs24\insrsid8198892 \cell }{\b\f0\fs24\insrsid8198892 q(x)}{\f0\fs24\insrsid8198892 \cell }\pard \ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\f0\fs24\insrsid8198892 \trowd 
\ts11\trgaph70\trleft-70\trkeep\trftsWidth1\trpaddl70\trpaddr70\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrtbl \clbrdrl\brdrtbl \clbrdrb\brdrtbl \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1134\clshdrawnil \cellx1064\clvertalt\clbrdrt\brdrtbl 
\clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrtbl \cltxlrtb\clftsWidth3\clwWidth1134\clshdrawnil \cellx2198\row }\trowd \lastrow \ts11\trgaph70\trleft-70\trkeep\trftsWidth1\trpaddl70\trpaddr70\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt
\brdrs\brdrw15 \clbrdrl\brdrtbl \clbrdrb\brdrtbl \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1134\clshdrawnil \cellx1064\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrtbl \clbrdrr\brdrtbl 
\cltxlrtb\clftsWidth3\clwWidth1134\clshdrawnil \cellx2198\pard \qc \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\b\f0\fs24\insrsid8198892 r}{\f0\fs24\insrsid8198892 \cell }{\b\f0\fs24\insrsid8198892 c(x)}{\f0\fs24\insrsid8198892 
\cell }\pard \ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\f0\fs24\insrsid8198892 \trowd \lastrow \ts11\trgaph70\trleft-70\trkeep\trftsWidth1\trpaddl70\trpaddr70\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl
\brdrtbl \clbrdrb\brdrtbl \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1134\clshdrawnil \cellx1064\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrtbl \clbrdrr\brdrtbl \cltxlrtb\clftsWidth3\clwWidth1134\clshdrawnil \cellx2198
\row }\pard \qc \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\b\f0\fs24\lang1046\langfe13322\langnp1046\insrsid8198892\charrsid8198892 p(x)=q(x).c(x)+r,   o bien,
\par 
\par }{\pard\plain \qc \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \fs24\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\object\objemb\objw2000\objh620{\*\objclass Equation.3}{\*\objdata 01050000020000000b000000
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00000500000014024002170807000000210501002b000000000010000000fb021000070000000000bc02000000000102022253797374656d0006040000002d01020004000000f0010100030000000000}{\result {\b\f0\fs24\dn26\insrsid8198892 
{\pict{\*\picprop\shplid1058{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}
\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw3528\pich1094\picwgoal2000\pichgoal620\wmetafile8\bliptag-1801821852\blipupi-277{\*\blipuid 949a6164215b2ac186273a9d1114d562}
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\par }\pard \qc \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\b\f0\fs24\insrsid8198892 
\par }\pard \qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\b\f0\fs24\insrsid8198892 Por tanto,
\par 
\par }\pard \qj \li708\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin708\itap0 {\pard\plain \qj \li708\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin708\itap0 \fs24\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\object\objemb
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{\pict{\*\picprop\shplid1059{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}
{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw4868\pich1270\picwgoal2760\pichgoal720\wmetafile8\bliptag-1140645554\blipupi360{\*\blipuid bc03214ee58503191efa1cb9306467e5}
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\par }\pard \qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\b\f0\fs24\insrsid8198892 
\par Veamos a trav\'e9s de ejemplos c\'f3mo se procede:
\par 
\par 
\par 
\par 
\par 
\par 
\par }\pard \qj \li0\ri0\widctlpar\brdrt\brdrs\brdrw15\brsp20 \brdrl\brdrs\brdrw15\brsp20 \brdrb\brdrs\brdrw15\brsp20 \brdrr\brdrs\brdrw15\brsp20 \aspalpha\aspnum\faauto\adjustright\rin0\lin0\rtlgutter\itap0 \shading2500\cbpat8 {\b\f0\fs24\insrsid8198892 a)  }
{\pard\plain \qj \li0\ri0\widctlpar\brdrt\brdrs\brdrw15\brsp20 \brdrl\brdrs\brdrw15\brsp20 \brdrb\brdrs\brdrw15\brsp20 \brdrr\brdrs\brdrw15\brsp20 \aspalpha\aspnum\faauto\adjustright\rin0\lin0\rtlgutter\itap0 
\fs24\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\object\objemb\objw1120\objh680{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e3300000000000000000080000000
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15000000fb0220ff0000000000009001000000000402001054696d6573204e657720526f6d616e000081040000002d01010004000000f001020008000000320af60072030100000032000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000
040000002d01020004000000f0010100030000000000}{\result {\b\f0\fs24\dn24\insrsid8198892 {\pict{\*\picprop\shplid1060{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}
{\sp{\sn fillColor}{\sv 12632256}}{\sp{\sn fFilled}{\sv 1}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}
\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw1976\pich1199\picwgoal1120\pichgoal680\wmetafile8\bliptag1766346546\blipupi-1454{\*\blipuid 69484f327e45b1ba7e24729d686baee4}
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526f6d616e000081040000002d01020004000000f001010008000000320ae603600401000000310008000000320ae603a80101000000320015000000fb0220ff
0000000000009001000000000402001054696d6573204e657720526f6d616e000081040000002d01010004000000f001020008000000320af600720301000000
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\par }\pard \qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\f0\fs24\ul\insrsid8198892 
\par }\pard \qj \li0\ri0\sl360\slmult1\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\f0\fs24\ul\insrsid8198892 Soluci\'f3n:
\par }\pard \qj \li0\ri0\sl360\slmult1\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\f0\fs24\insrsid8198892 Dado que el grado del numerador es mayor que el grado del denomina\-dor, hemos de realizar la divisi\'f3n c
on lo que se obtiene el siguiente cociente y resto:
\par }\pard \qj \li708\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin708\itap0 {\f0\fs24\insrsid8198892 
\par C(x)=}{\pard\plain \qj \li708\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin708\itap0 \fs24\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\object\objemb\objw760\objh580{\*\objclass Equation.3}{\*\objdata 01050000020000000b000000
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00002d01020004000000f0010100030000000000}{\result {\f0\fs24\dn22\insrsid8198892 {\pict{\*\picprop\shplid1061{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}
{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw1341\pich1023\picwgoal760\pichgoal580\wmetafile8\bliptag1536196531\blipupi2304{\*\blipuid 5b907fb3467cd230cdcd096f9e0e78d8}
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\qj \li708\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin708\itap0 \fs24\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\object\objemb\objw200\objh580{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e3300
00000000000000004000000002010101000a01030e000001028831000102883400000000ffffffffffffffff000000000000000000000000000000000000000000000000000000007fff3df301050000050000000d0000004d45544146494c4550494354006101000001fcffff3601000008006101ff030000
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fb021000070000000000bc02000000000102022253797374656d0006040000002d01020004000000f0010100030000000000}{\result {\f0\fs24\dn22\insrsid8198892 {\pict{\*\picprop\shplid1062{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw353\pich1023\picwgoal200\pichgoal580\wmetafile8\bliptag-72705526\blipupi2305{\*\blipuid fbaa9a0a5fb3dbfe980c0e80fae246a1}010009000003970000000300150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01190005000000310201000000
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\par }\pard \qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\f0\fs24\insrsid8198892 
\par }\pard \qj \li0\ri0\sl360\slmult1\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\f0\fs24\insrsid8198892 Como los denominadores son iguales los numeradaores tambi\'e9n lo ser\'e1n, por tanto,
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{\pict{\*\picprop\shplid1070{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}
{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw10724\pich1235\picwgoal6080\pichgoal700\wmetafile8\bliptag-2133647864\blipupi308{\*\blipuid 80d31e086b54c3db0bb99396f36ce328}
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\par }\pard \qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\f0\fs24\insrsid8198892 
\par 
\par }\pard \qj \li0\ri0\widctlpar\brdrt\brdrs\brdrw15\brsp20 \brdrl\brdrs\brdrw15\brsp20 \brdrb\brdrs\brdrw15\brsp20 \brdrr\brdrs\brdrw15\brsp20 \aspalpha\aspnum\faauto\adjustright\rin0\lin0\rtlgutter\itap0 \shading2500\cbpat8 {\b\f0\fs24\insrsid8198892 c)  }
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10000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01020004000000f0010100030000000000}{\result {\b\f0\fs24\dn32\insrsid8198892 {\pict{\*\picprop\shplid1071{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fillColor}{\sv 12632256}}{\sp{\sn fFilled}{\sv 1}}{\sp{\sn fHitTestFill}{\sv 1}}
{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw2046\pich1235\picwgoal1160\pichgoal700\wmetafile8\bliptag-1396732372\blipupi-1332{\*\blipuid acbf8e2c52b56f0333ceb38621b44074}
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\par }\pard \qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\f0\fs24\ul\insrsid8198892 
\par Soluci\'f3n:
\par }\pard \qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\f0\fs24\insrsid8198892 
\par En este caso la descomposici\'f3n en fracciones simples es m\'e1s sencilla:
\par 
\par }\pard \qj \li708\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin708\itap0 {\pard\plain \qj \li708\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin708\itap0 \fs24\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\object\objemb
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{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
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\par }\pard \qj \li708\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin708\itap0 {\f0\fs24\insrsid8198892 
\par }{\pard\plain \qj \li708\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin708\itap0 \fs24\lang1034\langfe13322\cgrid\langnp1034\langfenp13322 {\object\objemb\objw2060\objh280{\*\objclass Equation}{\*\objdata 010500000200000009000000
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{\pict{\*\picprop\shplid1073{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}
\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw3634\pich494\picwgoal2060\pichgoal280\wmetafile8\bliptag594819122\blipupi-586{\*\blipuid 23743832e833ec67974aa6f158d5d362}
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\par }\pard \qj \li708\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin708\itap0 {\f0\fs24\insrsid8198892 
\par Las raices del denominador son }{\b\f0\fs24\insrsid8198892 0 }{\f0\fs24\insrsid8198892 y }{\f0\fs24\insrsid8198892 {\field{\*\fldinst SYMBOL 45 \\f "Symbol" \\s 12}{\fldrslt\f3\fs24}}}{\b\f0\fs24\insrsid8198892 1:
\par }\pard \qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\f0\fs24\insrsid8198892 
\par }\pard \qc \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\f0\fs24\insrsid8198892 Para x= }{\f0\fs24\insrsid8198892 {\field{\*\fldinst SYMBOL 45 \\f "Symbol" \\s 12}{\fldrslt\f3\fs24}}}{\f0\fs24\insrsid8198892 1, b = 4
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