What is the integral from 0 to 1 of xe^{3x^2} ?

The integral from 0 to 1 of xe^{3x^2} is (e^3-1)/6

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integral from 0 to 1 of xe^{3x^2}

\int_{0}^{1} x e^{3 x^{2}} d x

\frac{e ^{3} - 1}{6}

Decimal

3.18092 \dots

Solution steps

\int_{0}^{1} x e^{3 x^{2}} d x

Apply u-substitution

= \int_{0}^{3} \frac{e ^{u}}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int_{0}^{3} e^{u} d u

Use the common integral:

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

= \frac{1}{6} [e^{u}]_{0}^{3}

Compute the boundaries:

e^{3} - 1

= \frac{1}{6} (e^{3} - 1)

Simplify

= \frac{e ^{3} - 1}{6}

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What is the integral from 0 to 1 of xe^{3x^2} ?
The integral from 0 to 1 of xe^{3x^2} is (e^3-1)/6