Question

Use the reduction formula for cosine to find the integral of cos(8x)^2dx and cos(8x)^4dx.

Answer 1

cos^2x = (1+cos2x)/2. So the first one just becomes (1+cos16x)/2, which you can reduce from there. For the second one you're forced to do it twice. Its the same deal, just requires more algebra and care.

Answer 2

Would you know how to go about integrating the first one after (1+cos16x)/2?