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Expert: - 1/21/2008


Question
We are doing integrals and I can not figure out these three...Can you help me?
1- the integral of x^13cox(x^7)dx -by substitution & integrations by parts
2- the integral of (ln(2x))^2dx -by integration by parts
3- the integral of 2y(tan^(-1)(7y))dy -by integration by parts

Answer
1. Let u=x^7, du=7x^6 dx.  Do another u substituion on the result, and it will be solved.

2. Take u=ln(2x).  Then du=2/x dx and x=(e^u)/2, so
dx=(e^u)/4 du.  The problem becomes the integral of
u^2(e^u)/4 du.  Do a couple of more u substituions with the new u being the term in front and dv being the exponential du.  This will reduce the u^2 to u to nothing leaving us with a few terms and an integral involving an e^u.

3. Try u=7y, dv=tan^-1(7y)dy.  Simplify and convert try another with u=x and dv=2sin(x)/(49cos^2(x)).

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