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

The integral from 0 to 1 of e^{5x} is (e^5-1)/5

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integral from 0 to 1 of e^{5x}

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

\frac{e ^{5} - 1}{5}

Decimal

29.48263 \dots

Solution steps

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

Apply u-substitution

= \int_{0}^{5} 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_{0}^{5} e^{u} d u

Use the common integral:

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

= \frac{1}{5} [e^{u}]_{0}^{5}

Compute the boundaries:

e^{5} - 1

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

Simplify

= \frac{e ^{5} - 1}{5}

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