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

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

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integral of (e^x+x^2)

\int (e^{x} + x^{2}) d x

e^{x} + \frac{x ^{3}}{3} + C

Solution steps

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

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

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

= e^{x} + \frac{x ^{3}}{3}

Add a constant to the solution

= e^{x} + \frac{x ^{3}}{3} + C