## anonymous 5 years ago Evaluate the integral of csc^2x + cscxcotx dx from pi/4 to pi/2

1. amistre64

do you know your trig derivatives?

2. amistre64

$\int\limits_{} \csc^2 + \csc(x)\cot(x) dx$

3. anonymous

yeah i know them. should i use u substitution?

4. amistre64

$D(\cot(x)) = \csc^2$$D(\csc(x)) = \csc(x)\cot(x)$

5. amistre64

no sub needed; just reverse them back up :)$\cot(x) + \csc(x) |_{\frac{\pi}{4}}^{\frac{\pi}{2}}$

6. anonymous

Thanks!

7. amistre64

the art of substitution and the like are used when we come across a ABnormal integral so that we can make it look like something we can manipulate. This? its already normal :)