What is the integral of csc^2(x)x ?

The integral of csc^2(x)x is -xcot(x)+ln|sin(x)|+C

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integral of csc^2(x)x

\int csc^{2} (x) x d x

- x cot (x) + ln ∣ sin (x) ∣ + C

Solution steps

\int csc^{2} (x) x d x

Apply Integration By Parts

: - x cot (x) - \int - cot (x) d x

= - x cot (x) - \int - cot (x) d x

\int - cot (x) d x = - ln ∣ sin (x) ∣

= - x cot (x) - (- ln ∣ sin (x) ∣)

Simplify

= - x cot (x) + ln ∣ sin (x) ∣

Add a constant to the solution

= - x cot (x) + ln ∣ sin (x) ∣ + C

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What is the integral of csc^2(x)x ?
The integral of csc^2(x)x is -xcot(x)+ln|sin(x)|+C