What is the integral of 3x^2+xe^x ?

The integral of 3x^2+xe^x is x^3+e^xx-e^x+C

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integral of 3x^2+xe^x

\int 3 x^{2} + x e^{x} d x

x^{3} + e^{x} x - e^{x} + C

Solution steps

\int 3 x^{2} + x e^{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 3 x^{2} d x + \int x e^{x} d x

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

\int x e^{x} d x = e^{x} x - e^{x}

= x^{3} + e^{x} x - e^{x}

Add a constant to the solution

= x^{3} + e^{x} x - e^{x} + C