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

The integral of (x^3+e^x) is (x^4)/4+e^x+C

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integral of (x^3+e^x)

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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