Question

Integrate the following w.r.t.x : `(1)/((1 - cos4x)(3 - cot2x)`

Answer 1

Let I = `int (1)/((1 - cos4x)(3 - cot2x))*dx`

= `int (1)/(2sin^2 2x(3 - cot2x))*dx`

= `(1)/(2) int ("cosec"^2x)/(3 - cot2x)*dx`

Put 3 – cot 2x = t
∴ 2 cosec²2x·dx = dt

∴ cosec²2x·dx = `(1)/(2)*dt`

∴ I = `(1)/(4) int 1/t*dt`

= `(1)/(4)log|t| + c`

= `(1)/(4)log|3 - cot2x| + c`.