document.write( "Question 1113322: Pls help \r
\n" ); document.write( "\n" ); document.write( "Use integration by parts to find \r
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\n" ); document.write( "\n" ); document.write( "∫ e^-x cosx dx \n" ); document.write( "
Algebra.Com's Answer #728352 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
In a message dated 3/27/2018 12:35:31 PM Eastern Standard Time, anlytcphil@aol.com writes:
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document.write( "Let I = \"int%28e%5E%28-x%29cos%28x%29%2Cdx%29\"\r\n" );
document.write( " u = cos(x) dv = e-xdx\r\n" );
document.write( "du = -sin(x) v = -e-x\r\n" );
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document.write( "I = uv - ∫vdu = cos(x)[-e-x] - ∫[-e-x][-sin(x)]\r\n" );
document.write( "I = -e-xcos(x) - ∫e-xsin(x)dx\r\n" );
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document.write( "Let J = \"int%28e%5E%28-x%29sin%28x%29%2Cdx%29\", then \r\n" );
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document.write( "I = -e-xcos(x) - J\r\n" );
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document.write( "Now we find J:\r\n" );
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document.write( "J = \"int%28e%5E%28-x%29sin%28x%29%2Cdx%29\"\r\n" );
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document.write( "u = sin(x)    dv = e-xdx\r\n" );
document.write( "du = cos(x)    v = -e-x\r\n" );
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document.write( "J = uv - ∫vdu = sin(x)[-e-x] - ∫[-e-x][cos(x)]\r\n" );
document.write( "J = -e-xsin(x) - ∫e-xcos(x)\r\n" );
document.write( "J = uv - ∫vdu = sin(x)[-e-x] - ∫[-e-x][cos(x)]\r\n" );
document.write( "J = -e-xsin(x) + ∫e-xcos(x)\r\n" );
document.write( "J = -e-xsin(x) + I\r\n" );
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document.write( "Substitute that for J in\r\n" );
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document.write( " I = -e-xcos(x) - J\r\n" );
document.write( " I = -e-xcos(x) -(-e-xsin(x) + I)\r\n" );
document.write( " I = -e-xcos(x) + e-xsin(x) - I\r\n" );
document.write( "2I = -e-xcos(x) + e-xsin(x)\r\n" );
document.write( "2I = e-x[-cos(x) + sin(x)]\r\n" );
document.write( "2I = e-x[sin(x) - cos(x)]\r\n" );
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document.write( "Final answer: \r\n" );
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document.write( "\"I\"\"%22%22=%22%22\"\"expr%281%2F2%29e%5E%28-x%29%28sin%28x%29%5E%22%22+-+cos%28x%29%29%2BC\"\r\n" );
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document.write( "Edwin
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