What is the integral of x/(sin^2(x)) ?

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

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integral of x/(sin^2(x))

integral

\frac{x}{sin ^{2} ( x )}

- x cot (x) + ln ∣ sin (x) ∣ + C

Solution steps

\int \frac{x}{sin ^{2} ( x )} d x

Apply Integration By Parts

= - 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

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