What is the integral of cot(θ)*ln(7sin(θ)) ?

The integral of cot(θ)*ln(7sin(θ)) is ln(7sin(θ))ln|sin(θ)|-(ln|sin(θ)|^2)/2+C

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integral of cot(θ)*ln(7sin(θ))

\int cot (θ) \cdot ln (7 sin (θ)) d θ

ln (7 sin (θ)) ln ∣ sin (θ) ∣ - \frac{ln ∣ sin ( θ ) ∣ ^{2}}{2} + C

Solution steps

\int cot (θ) ln (7 sin (θ)) d θ

Apply Integration By Parts

: ln (7 sin (θ)) ln ∣ sin (θ) ∣ - \int cot (θ) ln ∣ sin (θ) ∣ d θ

= ln (7 sin (θ)) ln ∣ sin (θ) ∣ - \int cot (θ) ln ∣ sin (θ) ∣ d θ

\int cot (θ) ln ∣ sin (θ) ∣ d θ = \frac{ln ∣ sin ( θ ) ∣ ^{2}}{2}

= ln (7 sin (θ)) ln ∣ sin (θ) ∣ - \frac{ln ∣ sin ( θ ) ∣ ^{2}}{2}

Add a constant to the solution

= ln (7 sin (θ)) ln ∣ sin (θ) ∣ - \frac{ln ∣ sin ( θ ) ∣ ^{2}}{2} + C

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What is the integral of cot(θ)*ln(7sin(θ)) ?
The integral of cot(θ)*ln(7sin(θ)) is ln(7sin(θ))ln|sin(θ)|-(ln|sin(θ)|^2)/2+C