Question

Evaluate: Integral of (sin^2 x cos ^3 x) dx.

The answer is (1/3)sin^3 x - (1/5) sin^5 x + C

Need help with how to get to the answer.

Answer 1

i think you can rewrite \(\cos^3(x)\) as \((1-\sin^2(x))\cos(x)\)

Answer 2

then you get
\[\int \sin^2(x)(1-\sin^2(x))\cos(x)dx\] and u - sub via \(u=\sin(x), du=\cos(x)dx\)

Answer 3

I'll try it right now.

Answer 4

ok, should work

Answer 5

yep, it does. Thank you!