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

The integral of x^2csc^2(x)cot(x) is -1/2 x^2csc^2(x)-xcot(x)+ln|sin(x)|+C

Popular >

integral of x^2csc^2(x)cot(x)

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

- \frac{1}{2} x^{2} csc^{2} (x) - x cot (x) + ln ∣ sin (x) ∣ + C

Solution steps

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

Apply Integration By Parts

: - \frac{1}{2} x^{2} csc^{2} (x) - \int - x csc^{2} (x) d x

= - \frac{1}{2} x^{2} csc^{2} (x) - \int - x csc^{2} (x) d x

\int - x csc^{2} (x) d x = x cot (x) - ln ∣ sin (x) ∣

= - \frac{1}{2} x^{2} csc^{2} (x) - (x cot (x) - ln ∣ sin (x) ∣)

Simplify

= - \frac{1}{2} x^{2} csc^{2} (x) - x cot (x) + ln ∣ sin (x) ∣

Add a constant to the solution

= - \frac{1}{2} x^{2} csc^{2} (x) - x cot (x) + ln ∣ sin (x) ∣ + C

\int + sin^{3} (x) cos^{14} (x) d x

\frac{3 x}{x - \frac{3}{x}}

\frac{35}{4 + x + x}

\frac{d}{d x} (\frac{x - 6}{x + 4})

x \to \infty lim (4 (x - 3))

What is the integral of x^2csc^2(x)cot(x) ?
The integral of x^2csc^2(x)cot(x) is -1/2 x^2csc^2(x)-xcot(x)+ln|sin(x)|+C