integral problem?

Question

integral of (sinx)^4*(cotx)^3

help please.

Answer 1

cotx = cosx/sinx

y = integral of (sinx)^4*(cotx)^3
= integral of (sinx)^4*(cosx)^3/(sinx)^3
= integral of sinx*(cosx)^3

let cosx = u
sinxdx = du

so, y = integral of u^3 du
= (u^4)/4
= (1/4)(cosx)^4 + constant

Answer 2

(sinx)^4*(cotx)^3
= sin^4(x) * [cos^3(x) / sin^3(x)]
= cos^3(x) sin(x)

Let u = cos^3x
du = -sinx dx

-1∫ cos^3(x) (-sin(x)) dx
= -1/4 cos^4x + c