Question

Evaluate the integral of csc^2x + cscxcotx dx from pi/4 to pi/2

Answer 1

do you know your trig derivatives?

Answer 2

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

Answer 3

yeah i know them. should i use u substitution?

Answer 4

\[D(\cot(x)) = \csc^2\]\[D(\csc(x)) = \csc(x)\cot(x)\]

Answer 5

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

Answer 6

Thanks!

Answer 7

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 :)