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

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

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integral of cos(x)sin(x)+x^2

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

\frac{sin ^{2} ( x )}{2} + \frac{x ^{3}}{3} + C

Solution steps

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

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

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

= \frac{sin ^{2} ( x )}{2} + \frac{x ^{3}}{3}

Add a constant to the solution

= \frac{sin ^{2} ( x )}{2} + \frac{x ^{3}}{3} + C

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