Question

Please help me in this integration prob.
integrate (5 cos^5 (x)) / (sin^7 (x))

Answer 1

\[\frac{\cos^5(x)}{\sin^7(x)}=\cot^5(x) \csc^2(x) \\ \text{ recall the following } \\ \frac{d}{dx} \cot(x)=-\csc^2(x) \\ \frac{d}{dx} \csc(x)=-\cot(x) \csc(x) \\ \text{ looks like the first one is going to be the one you want! :)}\]

\[\text{ Let } u=\cot(x)\]

Answer 2

Did u get it @pat12345 ?

Answer 3

so, cot^2 x . csc^2 x . du/csc^2 x
= int u^2 du
=int (u^3)/3 +c
=(cot^3)/3 +C is correct ans ?

Answer 4

what happen to the 5th power on the cotangent function ?

Answer 5

sorry! so, after cancelling scs^2 it will be int -5u^5 du
= (-5u^6)/6 +C
= -5/6 cot^6 x +C

Answer 6

Thank you.

Answer 7

my notifications aren't working :p
but yep that looks amazing! :)