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

= - 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

\int 5 x - 6 d x

\frac{x}{x ^{2} + 6}

[x - y arctan (\frac{y}{x})] d x + x arctan (\frac{y}{x}) d y = 0

\int_{7}^{\infty} x e^{- 2 x} d x

t y^{^{'}} + 2 y = t^{2}

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