Evaluate the Integral. Show All Steps

Question

Evaluate the Integral. Show All Steps. If possible attach a video going through the problem.

Answer 1

sinx = u; x = π/6, u = 1/2; x = π/2, u = 1; cosxdx = du

∫_π/6^π/2cos⁵x/sin⁶xdx = ∫_1/2¹(1 - u²)²/u⁶du =∫_1/2¹(u^-6 - 2u^-4 + u^-2)du = (u^-5/(-5) - 2u^-3/(-3) + u^-1/(-1))_1/2¹ = - 8/15 + 46/15 = 38/15