What is the integral of θcsc^2(θ) ?

The integral of θcsc^2(θ) is -θcot(θ)+ln|sin(θ)|+C

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integral of θcsc^2(θ)

\int θ csc^{2} (θ) d θ

- θ cot (θ) + ln ∣ sin (θ) ∣ + C

Solution steps

\int θ csc^{2} (θ) d θ

Apply Integration By Parts

= - θ cot (θ) - \int - cot (θ) d θ

\int - cot (θ) d θ = - ln ∣ sin (θ) ∣

= - θ cot (θ) - (- ln ∣ sin (θ) ∣)

Simplify

= - θ cot (θ) + ln ∣ sin (θ) ∣

Add a constant to the solution

= - θ cot (θ) + ln ∣ sin (θ) ∣ + C

What is the integral of θcsc^2(θ) ?
The integral of θcsc^2(θ) is -θcot(θ)+ln|sin(θ)|+C