What is the integral from 0 to 1 of [e^{5x+3}] ?

The integral from 0 to 1 of [e^{5x+3}] is (e^8-e^3)/5

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integral from 0 to 1 of [e^{5x+3}]

\int_{0}^{1} [e^{5 x + 3}] d x

\frac{e ^{8} - e ^{3}}{5}

Decimal Notation

592.17449 \dots

Solution steps

\int_{0}^{1} e^{5 x + 3} d x

Apply u-substitution

: \int_{3}^{8} e^{u} \frac{1}{5} d u

= \int_{3}^{8} e^{u} \frac{1}{5} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{5} \cdot \int_{3}^{8} e^{u} d u

Use the common integral:

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

= \frac{1}{5} [e^{u}]_{3}^{8}

Compute the boundaries:

e^{8} - e^{3}

= \frac{1}{5} (e^{8} - e^{3})

Simplify

= \frac{e ^{8} - e ^{3}}{5}

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What is the integral from 0 to 1 of [e^{5x+3}] ?
The integral from 0 to 1 of [e^{5x+3}] is (e^8-e^3)/5