Please help me solve this with a detailed solution Evaluate

Please help me solve this with a detailed solution. Evaluate the following integral (no Integral Tables).

sin 6 x sin 2xdx (Hint: sin mx sin nx = 1 / 2 [cos(m - n)x - cos(m + n)x])

Solution

sin6xsin2x = 1/2[cos4x - cos8x] integration(sin6xsin2x)dx = integration(1/2[cos4x - cos8x])dx = 1/8sin4x - 1/16sin8x + C