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

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

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

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

\frac{3 ( e - 1 )}{2}

Decimal

2.57742 \dots

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int_{0}^{1} \frac{e ^{u}}{2} d u

= 3 \cdot \int_{0}^{1} \frac{e ^{u}}{2} d u

Take the constant out:

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

= 3 \cdot \frac{1}{2} \cdot \int_{0}^{1} e^{u} d u

Use the common integral:

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

= 3 \cdot \frac{1}{2} [e^{u}]_{0}^{1}

Simplify

3 \cdot \frac{1}{2} [e^{u}]_{0}^{1} : \frac{3}{2} [e^{u}]_{0}^{1}

= \frac{3}{2} [e^{u}]_{0}^{1}

Compute the boundaries:

e - 1

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

Simplify

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

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