What is the integral from 1 to 3 of (x+1)e^{x^2+2x} ?

The integral from 1 to 3 of (x+1)e^{x^2+2x} is (e^{15}-e^3)/2

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integral from 1 to 3 of (x+1)e^{x^2+2x}

\int_{1}^{3} (x + 1) e^{x^{2} + 2 x} d x

\frac{e ^{15} - e ^{3}}{2}

Decimal

1634498.64346 \dots

Solution steps

\int_{1}^{3} (x + 1) e^{x^{2} + 2 x} d x

Apply u-substitution

: \int_{3}^{15} \frac{e ^{u}}{2} d u

= \int_{3}^{15} \frac{e ^{u}}{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_{3}^{15} e^{u} d u

Use the common integral:

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

= \frac{1}{2} [e^{u}]_{3}^{15}

Compute the boundaries:

e^{15} - e^{3}

= \frac{1}{2} (e^{15} - e^{3})

Simplify

= \frac{e ^{15} - e ^{3}}{2}

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What is the integral from 1 to 3 of (x+1)e^{x^2+2x} ?
The integral from 1 to 3 of (x+1)e^{x^2+2x} is (e^{15}-e^3)/2