document.write( "Question 918565: integration of x*sec(x)dx \n" ); document.write( "
Algebra.Com's Answer #557130 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"int%28x%2Asec%28x%29dx%29\"\r\n" );
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document.write( "By parts:\r\n" );
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document.write( "\"u=x\",  \"dv=sec%28x%29dx\"\r\n" );
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document.write( "\"du=dx\",  \"int%28dv%29\"\"%22%22=%22%22\"\"int%28sec%28x%29dx%29\"\r\n" );
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document.write( "\"u=x\",  \"v=ln%28sex%28x%29%2Btan%28x%29%29\"\r\n" );
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document.write( "\"int%28x%2Asec%28x%29dx%29\"\"%22%22=%22%22\"\"uv-int%28v%2Adu%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "\"x%2Aln%28sec%28x%29%2Btan%28x%29%29-int%28ln%28abs%28secx%2Btan%28x%29%29%29dx%29\"\r\n" );
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document.write( "But there is no ordinary formula for that.  So this problem cannot be \r\n" );
document.write( "done by the methods of an ordinary calculus course.  There are advanced \r\n" );
document.write( "methods that deal with polylogarithm functions that allow this to be\r\n" );
document.write( "integrated.  But an ordinary calculus course should not give a problem\r\n" );
document.write( "such as this.  Maybe a definite integral of this same expression that \r\n" );
document.write( "could approximated by the trapezoid method or Simpson's rule would be\r\n" );
document.write( "OK.  Talk with your instructor about this.\r\n" );
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document.write( "Edwin
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