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