Question

Integrate the following function: cot x log sin x

Answer 1

Please see the attachment

Answer 2

Integrate the following function: cot x log sin x

solution : we have to integrate , ∫cotx. log(sinx) dx

let log(sinx) = p .......(1)

differentiating both sides ,

1/sinx × (cosx) = dp/dx

or, cosx/sinx = dp/dx

or, cotx dx = dp ......(2)

putting the equations (1) and (2) in ∫cotx . log(sinx) dx .

now, ∫cotx . log(sinx) dx converts into ∫p dp

∫p dp = p²/2 + K

where k is constant.

now, put p = log(sinx)

then, ∫cotx .log(sinx) dx = {log(sinx)}²/2 + K .