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

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

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integral of xcsc^2(x)

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

- x cot (x) + ln ∣ sin (x) ∣ + C

Solution steps

\int x csc^{2} (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

(x + 2 y^{2}) d x + (x y) d y = 0

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\int cos (\frac{2 πn x}{L}) d x

\int \frac{1}{5 x - 1} d x

x \to \infty + lim ((1 + 2 x)^{\frac{1}{2 l n ( x )}})

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