math
posted by daniel on .
integration of
cot^4(12x)dx

cot^4(12x) dx =
= cot^2(12x)*cot^2(12x) dx
= {cosec^2(12x)  1}*cot^2(12x) dx
= cosec^2(12x)*cot^2(12x) dx  cot^2(12x) dx
= cosec^2(12x)*cot^2(12x) d(cot(12x))/(cosec^2(12x)*(2))  {cosec^2(12x)  1} dx
= (1/2)cot^2(12x) d(cot(12x))  cosec^2(12x) dx + dx
= (1/6)cot^3(12x)  (1/2)cot(12x) + x + const