∫ 1/(sinxcosx)^4 dx
=∫ 1/(1/2sin2x)^4 dx
=16∫ 1/(sin2x)^4 dx
=16∫ (csc2x)^4 dx
=-8∫ (csc2x)^2 d(cot2x)
=-8∫ (1+(cot2x)^2) d(cot2x)
=-8cot2x-8/3(cot2x)^3+C
∫ 1/(sinxcosx)^4 dx
=∫ 1/(1/2sin2x)^4 dx
=16∫ 1/(sin2x)^4 dx
=16∫ (csc2x)^4 dx
=-8∫ (csc2x)^2 d(cot2x)
=-8∫ (1+(cot2x)^2) d(cot2x)
=-8cot2x-8/3(cot2x)^3+C