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 \to + (- 2) lim (\frac{- 9}{x ^{2}})

2 \leq x \leq 6, y = 2

x^{4} cos (7 x - 5)

2 a y

f (x) = e^{y^{2}} + 2 x^{3}

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