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

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

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

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

\frac{e - 1}{2 e}

Decimal

0.31606 \dots

Solution steps

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

Apply u-substitution

= \int_{- 1}^{0} \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}^{0} e^{u} d u

Use the common integral:

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

= \frac{1}{2} [e^{u}]_{- 1}^{0}

Compute the boundaries:

1 - \frac{1}{e}

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

Simplify

= \frac{e - 1}{2 e}

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