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

The integral of (e^{2x}+x^3) is 1/2 e^{2x}+(x^4)/4+C

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integral of (e^{2x}+x^3)

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

\frac{1}{2} e^{2 x} + \frac{x ^{4}}{4} + C

Solution steps

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

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

\int x^{3} d x = \frac{x ^{4}}{4}

= \frac{1}{2} e^{2 x} + \frac{x ^{4}}{4}

Add a constant to the solution

= \frac{1}{2} e^{2 x} + \frac{x ^{4}}{4} + C

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What is the integral of (e^{2x}+x^3) ?
The integral of (e^{2x}+x^3) is 1/2 e^{2x}+(x^4)/4+C