Evaluate the integrals using u-substitution:

Question

Evaluate the integrals using u-substitution:

∫sin^5(x/3)cos(x/3)dx

Answer 1

∫ sin⁵(x/3) cos(x/3) dx

Let u = sin(x/3). Then du = (1/3)cos(x/3)dx. So, cos(x/3)dx = 3du.

∫ sin⁵(x/3) cos(x/3)dx = 3 ∫ u⁵du = (1/2)u⁶ + C = (1/2)sin⁶(x/3) + C