What is the integral of e^{2x}+x^2 ?

The integral of e^{2x}+x^2 is 1/2 e^{2x}+(x^3)/3+C

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integral of e^{2x}+x^2

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

\frac{1}{2} e^{2 x} + \frac{x ^{3}}{3} + C

Solution steps

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

\int e^{2 x} d x = \frac{1}{2} e^{2 x}

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

= \frac{1}{2} e^{2 x} + \frac{x ^{3}}{3}

Add a constant to the solution

= \frac{1}{2} e^{2 x} + \frac{x ^{3}}{3} + C

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What is the integral of e^{2x}+x^2 ?
The integral of e^{2x}+x^2 is 1/2 e^{2x}+(x^3)/3+C