(SIN^8X-5 SIN^5X+SINX)COSX DX

Question

I need the answer to this, because I have tried so many times and cannot figure it out.

Answer 1

I infer from the presence of DX that you want

∫(sin^8(x) - 5sin^5(x) + sin(x)) cos(x) dx

if you let u = sin(x), then du = cos(x) dx you have

∫(u^8 - 5u^5 + u) du

that's dead easy, using thge power rule:

1/9 u^9 - 1/6 u^6 + 1/2 u^2 + C

now change all the u's back to sin(x) and you're done