# How the heck do I integrate this?

• May 23rd 2008, 12:33 PM
CrazyLond
How the heck do I integrate this?
I just got done taking a midterm from (Swear). Anyway, I managed to at least start most of the problems but this one just blew me away. I tried using some identities, etc. to make it look less evil but was not able to.

http://img81.imageshack.us/img81/990/midtermqfc0.jpg
• May 23rd 2008, 12:50 PM
galactus
One way is to use parts.

Let $u=x, \;\ dv=csc^{2}(2x)dx, \;\ du=dx, \;\ v=\frac{-1}{2}cot(2x)dx$

$\frac{-1}{2}xcot(2x)+\frac{1}{2}\int{cot(2x)}dx$

Take note that $\int{cot(u)}dx=ln|sin(u)|+C$