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

The integral of sin(x)*x^2 is -x^2cos(x)+2(xsin(x)+cos(x))+C

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integral of sin(x)*x^2

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

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

Solution steps

\int sin (x) x^{2} 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 \frac{8}{x x ^{2} - 1} d x

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\int \frac{x - 1}{x ^{2} - 1} d x

\int \frac{1}{1 - sin ^{4} ( x )} d x

\int \frac{cos ( 6 t )}{6 t} d t

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