What is the integral of (2e^x-x^3) ?

The integral of (2e^x-x^3) is 2e^x-(x^4)/4+C

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integral of (2e^x-x^3)

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

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

Solution steps

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

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

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

= 2 e^{x} - \frac{x ^{4}}{4}

Add a constant to the solution

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

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