Evaluate: intergral cos x sin^5 x dx?

Answer 1

Do you know the integral of sin^5 x? Probably not. Do you know the integral of cos x? Yes. It is sin x. So set u = sin x. Then du = cos x dx. The result is

∫ u^5 du.

That is u^6/6. Now substitute sin x for u. The result is:

sin^6 x / 6 + C

where C is an arbitrary constant.

Answer 2

Dear it is so easy
intergral cos x sin(x)^5 x dx
= intergral sin^5 x d sin(x)
= 1/6 sin^6 + constant