What is the integral of 7θcsc^2(θ) ?

The integral of 7θcsc^2(θ) is 7(-θcot(θ)+ln|sin(θ)|)+C

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integral of 7θcsc^2(θ)

\int 7 θ csc^{2} (θ) d θ

7 (- θ cot (θ) + ln ∣ sin (θ) ∣) + C

Solution steps

\int 7 θ csc^{2} (θ) d θ

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 7 \cdot \int θ csc^{2} (θ) d θ

Apply Integration By Parts

: - θ cot (θ) - \int - cot (θ) d θ

= 7 (- θ cot (θ) - \int - cot (θ) d θ)

\int - cot (θ) d θ = - ln ∣ sin (θ) ∣

= 7 (- θ cot (θ) - (- ln ∣ sin (θ) ∣))

Simplify

= 7 (- θ cot (θ) + ln ∣ sin (θ) ∣)

Add a constant to the solution

= 7 (- θ cot (θ) + ln ∣ sin (θ) ∣) + C

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What is the integral of 7θcsc^2(θ) ?
The integral of 7θcsc^2(θ) is 7(-θcot(θ)+ln|sin(θ)|)+C