What is the integral from 4 to 7 of e^{2x+1} ?

The integral from 4 to 7 of e^{2x+1} is (e^{15}-e^9)/2

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integral from 4 to 7 of e^{2x+1}

\int_{4}^{7} e^{2 x + 1} d x

\frac{e ^{15} - e ^{9}}{2}

Decimal

1630457.14427 \dots

Solution steps

\int_{4}^{7} e^{2 x + 1} d x

Apply u-substitution

= \int_{9}^{15} e^{u} \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{9}^{15} e^{u} d u

Use the common integral:

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

= \frac{1}{2} [e^{u}]_{9}^{15}

Compute the boundaries:

e^{15} - e^{9}

= \frac{1}{2} (e^{15} - e^{9})

Simplify

= \frac{e ^{15} - e ^{9}}{2}

What is the integral from 4 to 7 of e^{2x+1} ?
The integral from 4 to 7 of e^{2x+1} is (e^{15}-e^9)/2