How do you integrate #sin^2(x) cos^5(x)#?
Recommended: learn this pattern.
Pull off one from the odd power. (If both are odd, it is simpler, but not necessary, to make the lesser power even.)
Change the remaining even power to the other function using
Expand and substitute to get a polynomial in
It may sound complicated, but here's how it works for this question:
We are going to use
Our integral becomes:
# = int (sin^2x-2sin^3x+sin^4x) cosx dx#
# = int (u^2-2u^3+u^4) du = u^3/3+u^4/2+u^5/5+C#
# = sin^3x/3+sin^4x/2+sin^5x/5 +C#