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

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

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integral of-x^2*sin(x)

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply Integration By Parts

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

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

Add a constant to the solution

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

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