SOLUTION: integration of x*sec(x)dx

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Question 918565: integration of x*sec(x)dx
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
int%28x%2Asec%28x%29dx%29

By parts:

u=x,  dv=sec%28x%29dx

du=dx,  int%28dv%29%22%22=%22%22int%28sec%28x%29dx%29

u=x,  v=ln%28sex%28x%29%2Btan%28x%29%29

int%28x%2Asec%28x%29dx%29%22%22=%22%22uv-int%28v%2Adu%29%22%22=%22%22

x%2Aln%28sec%28x%29%2Btan%28x%29%29-int%28ln%28abs%28secx%2Btan%28x%29%29%29dx%29

But there is no ordinary formula for that.  So this problem cannot be 
done by the methods of an ordinary calculus course.  There are advanced 
methods that deal with polylogarithm functions that allow this to be
integrated.  But an ordinary calculus course should not give a problem
such as this.  Maybe a definite integral of this same expression that 
could approximated by the trapezoid method or Simpson's rule would be
OK.  Talk with your instructor about this.

Edwin