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

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

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

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

- x cot (x) + ln ∣ sin (x) ∣ + C

Solution steps

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

Rewrite using trig identities

= \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

\int x e^{x} + e^{x} d x

\int 2 sin^{2} (y) d y

\frac{d y}{d x} = \frac{y ^{2} - 1}{x ^{2} - 1}, y (2) = - 1

\frac{d}{d x} (ln^{4} (x^{3} + 2 x - e^{- 3 x}))

\frac{\partial}{\partial y} (1 + ln (x y))

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