What is the integral of x^2cos(x)-xsin(x) ?

The integral of x^2cos(x)-xsin(x) is x^2sin(x)-3(-xcos(x)+sin(x))+C

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integral of x^2cos(x)-xsin(x)

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

x^{2} sin (x) - 3 (- x cos (x) + sin (x)) + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

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

Simplify

= x^{2} sin (x) - 3 (- x cos (x) + sin (x))

Add a constant to the solution

= x^{2} sin (x) - 3 (- x cos (x) + sin (x)) + C

What is the integral of x^2cos(x)-xsin(x) ?
The integral of x^2cos(x)-xsin(x) is x^2sin(x)-3(-xcos(x)+sin(x))+C