Question

integration of
cot^4(1-2x)dx

Answer 1

|cot^4(1-2x) dx =
= |cot^2(1-2x)*cot^2(1-2x) dx
= |{cosec^2(1-2x) - 1}*cot^2(1-2x) dx
= |cosec^2(1-2x)*cot^2(1-2x) dx - |cot^2(1-2x) dx
= |cosec^2(1-2x)*cot^2(1-2x) d(cot(1-2x))/(-cosec^2(1-2x)*(-2)) - |{cosec^2(1-2x) - 1} dx
= (1/2)|cot^2(1-2x) d(cot(1-2x)) - |cosec^2(1-2x) dx + |dx
= (1/6)cot^3(1-2x) - (1/2)cot(1-2x) + x + const