What is the integral from 1 to 3 of xe^{x^2} ?

The integral from 1 to 3 of xe^{x^2} is (e^9-e)/2

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integral from 1 to 3 of xe^{x^2}

\int_{1}^{3} x e^{x^{2}} d x

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

Decimal

4050.18282 \dots

Solution steps

\int_{1}^{3} x e^{x^{2}} d x

Apply u-substitution

= \int_{1}^{9} \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_{1}^{9} e^{u} d u

Use the common integral:

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

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

Compute the boundaries:

e^{9} - e

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

Simplify

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

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What is the integral from 1 to 3 of xe^{x^2} ?
The integral from 1 to 3 of xe^{x^2} is (e^9-e)/2