What is the integral from 0 to 3 of (e^{2x}+x^3) ?

The integral from 0 to 3 of (e^{2x}+x^3) is (e^6-1)/2+81/4

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integral from 0 to 3 of (e^{2x}+x^3)

\int_{0}^{3} (e^{2 x} + x^{3}) d x

\frac{e ^{6} - 1}{2} + \frac{81}{4}

Decimal Notation

221.46439 \dots

Solution steps

\int_{0}^{3} 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_{0}^{3} e^{2 x} d x + \int_{0}^{3} x^{3} d x

\int_{0}^{3} e^{2 x} d x = \frac{e ^{6} - 1}{2}

\int_{0}^{3} x^{3} d x = \frac{81}{4}

= \frac{e ^{6} - 1}{2} + \frac{81}{4}

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What is the integral from 0 to 3 of (e^{2x}+x^3) ?
The integral from 0 to 3 of (e^{2x}+x^3) is (e^6-1)/2+81/4