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

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

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integral of x^2-sin(x)

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

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

Solution steps

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

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

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

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

Simplify

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

Add a constant to the solution

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

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