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Question

Mathematics Question on integral

Integrate the function: cot x.log sin xcot \ x .log\ sin\ x

Answer

Let log sin x=tLet\ log \ sin \ x = t
⇒1sin x.cosx dx=dt⇒ \frac {1}{sin\ x}.cos x\ dx = dt
∴cotx dx=dt∴ cot x \ dx = dt
⇒∫cot x.log sinx dx=∫tdt⇒ ∫cot \ x .log \ sin x \ dx = ∫t dt

                                      $=$ $\frac {t^2}{2}+C$

                                      $=$ $\frac 12(log \ sin x)^2 +C$