your completing the square part is fine. after this you will need to
-spilt up the fraction
-take out the constants of integration
-do a u substitution for the 2x part of numerator
-use arctan for the 4 part of the numerator
you will notice the the part you completed the square looks...
I had a similar question earlier. The result is a whole bunch of sine and cosine integrals and imaginary parts. I don't understand how one would do this, but go ahead and put it in the integrator (mathematica) and check the answer out. What level is this for?
Thank you. This seems more probable. Is there anyway you can show me how to actually integrate this function or suggest any sites that would show how to evaluate these type of integrals.
after the first integration by parts i get xln|sin(x)|-\intln|sin(x)|dx
using parts again, with u(x)=ln|sin(x)|, i get xln|sin(x)|-xln|sin(x)|-\intx/tanx dx
this is exactly where i started.
I entered this in an online integrator and got this as the answer...
Can someone please explain how to compute this integral? This is not for school; I just came across it and I'm not sure what to do. Parts and various identities didn't help. \int x/tan(x) dx