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

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

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integral of x^2-xsin(x)

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

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

Solution steps

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

\int x^{2} d x = \frac{x ^{3}}{3}

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

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

Simplify

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

Add a constant to the solution

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

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