How do I evaluate the indefinite integral ∫sin3(x)⋅cos2(x)dx ?
1 Answer
Sep 21, 2014
The answer is
The trick with sinusoidal powers is to use identities so that you can have
In this case, it is easier to get
∫sin3x⋅cos2xdx
=∫sinx(1−cos2x)cos2xdx
=∫sinx(cos2x−cos4x)dx
=∫sinxcos2xdx−∫sinxcos4xdx
Now it is a matter of using substitution:
u=cosx
du=−sinxdx
∫sinxcos2xdx−∫sinxcos4xdx
=∫−u2du+∫u4du
=−u33+u55+C
=−cos3x3+cos5x5+C