document.write( "Question 85524: If f'(x) = e^(2x)sin(x) ... what does f(x) equal? Please explain using antiderividants, integration by parts, and algebraic manipulation. \n" ); document.write( "
Algebra.Com's Answer #61757 by Nate(3500)\"\" \"About 
You can put this solution on YOUR website!
f'(x) = e^(2x)sin(x)
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\n" ); document.write( "[u = e^(2x)
\n" ); document.write( "[du = 2*e^(2x) dx
\n" ); document.write( "[dv = sin(x)
\n" ); document.write( "[v = - cos(x)
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\n" ); document.write( "\"int%28+e%5E%282x%29sin%28x%29%2C+dx%2Ca%2Cb%29\"
\n" ); document.write( "\"-e%5E%282x%29cos%28x%29+-+int%28+-2%2Ae%5E%282x%29%2Acos%28x%29+%2C+dx%2Ca%2Cb%29\"
\n" ); document.write( "\"-e%5E%282x%29cos%28x%29+%2B+2%2Aint%28+e%5E%282x%29%2Acos%28x%29+%2C+dx%2Ca%2Cb%29\"
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\n" ); document.write( "[u = e^(2x)
\n" ); document.write( "[du = 2*e^(2x) dx
\n" ); document.write( "[dv = cos(x)
\n" ); document.write( "[v = sin(x)
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\n" ); document.write( "\"-e%5E%282x%29cos%28x%29+%2B+2%2Aint%28+e%5E%282x%29%2Acos%28x%29+%2C+dx%2Ca%2Cb%29\"
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\n" ); document.write( "\"y+=+int%28+e%5E%282x%29sin%28x%29%2C+dx%2Ca%2Cb%29\"
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\n" ); document.write( "\"y+=+-e%5E%282x%29cos%28x%29+%2B+2e%5E%282x%29sin%28x%29+-+4y\"
\n" ); document.write( "\"5y+=+e%5E%282x%29%282%2Asin%28x%29+-+cos%28x%29%29\"
\n" ); document.write( "\"y+=+%281%2F5%29e%5E%282x%29%282%2Asin%28x%29+-+cos%28x%29%29\"
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\n" ); document.write( "Constant Rule:
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\n" ); document.write( "\"y+=+%281%2F5%29e%5E%282x%29%282%2Asin%28x%29+-+cos%28x%29%29+%2B+C\"
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