integral of 2sin^3xcosx dx

that is a sin cubed x. i think i use u-substituion, but im not quite sure how to do it. please help and thank you!

1 answer

Whenever there is an odd power of sin or cos in a product, you could use the substition u=sin(x) or u=cos(x).
This is a case of u=sin(x), since
du=cos(x)dx
Substituting in the given expression gives
∫u³du
If you are working on a definite integral, do not forget to substitute the limits as well.

I'm sure you can take it from here.