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

The integral of (x^2)/(csc(x)) is -x^2cos(x)+2(xsin(x)+cos(x))+C

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

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

- x^{2} cos (x) + 2 (x sin (x) + cos (x)) + C

Solution steps

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

Use the basic trigonometric identity:

\frac{1}{csc ( x )} = sin (x)

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

Apply Integration By Parts

: - x^{2} cos (x) - \int - 2 x cos (x) d x

= - x^{2} cos (x) - \int - 2 x cos (x) d x

\int - 2 x cos (x) d x = - 2 (x sin (x) + cos (x))

= - x^{2} cos (x) - (- 2 (x sin (x) + cos (x)))

Simplify

= - x^{2} cos (x) + 2 (x sin (x) + cos (x))

Add a constant to the solution

= - x^{2} cos (x) + 2 (x sin (x) + cos (x)) + C

\int_{0}^{5} \frac{1}{x ^{\frac{19}{20}}} d x

\int_{0}^{4} (6 - x^{2}) d x

x \to \infty lim (0. 1^{x})

x^{2} - \frac{1}{2} cos (x)

f (x) = (x^{4} + 3) (- 4 x^{5} + 5 x^{4} + 5)

What is the integral of (x^2)/(csc(x)) ?
The integral of (x^2)/(csc(x)) is -x^2cos(x)+2(xsin(x)+cos(x))+C