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

The integral from 0 to 3 of (e^x+x) is e^3+7/2

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

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

e^{3} + \frac{7}{2}

Decimal

23.58553 \dots

Solution steps

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

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

\int_{0}^{3} x d x = \frac{9}{2}

= e^{3} - 1 + \frac{9}{2}

Combine the fractions

- 1 + \frac{9}{2} : \frac{7}{2}

= e^{3} + \frac{7}{2}

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What is the integral from 0 to 3 of (e^x+x) ?
The integral from 0 to 3 of (e^x+x) is e^3+7/2