Solve the Trig Integral. ∫sin^2(x)cos^4(x) dx

Question

Solve the Trig Integral. Show all steps. If possible can you attach a video going through the process step by step.

∫sin²(x)cos⁴(x) dx

Answer 1

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Answer 2

∫sin²(x)cos⁴(x) dx = ∫(1 - cos2x)/2·(1 + cos2x)²/4dx = 1/8∫sin²2x(1 + cos2x)dx = 1/8∫[(1 + cos4x)/2 + sin²2xcos2x}dx = 1/16(x + sin4x/4) + sin³2x/48 + C = x/16 + sin4x/64 + sin^{32x/48 + C}