Evaluate the integral

Question

∫cos⁵(21x)/ sin³(21x) dx

Answer 1

Let u = sin(21x) Then du = 21cos(21x)dx therefore, cos(21x)dx = (1/21)du

cos²(21x) = 1 - sin²(21x) = 1 - u²

So, we have (1/21)∫ [(1 - u²)² / u³ ]du

= (1/21) ∫ [ (1 - 2u² + u⁴) / u³ ] du = (1/21) ∫ (u^-3 - 2u^-1 + u) du

You can take it from there.