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

The integral from 1 to 2 of 3xe^{3x^2-1} is (e^{11}-e^2)/2

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

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

\frac{e ^{11} - e ^{2}}{2}

Decimal Notation

29933.37632 \dots

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int_{2}^{11} \frac{e ^{u}}{6} d u

= 3 \cdot \int_{2}^{11} \frac{e ^{u}}{6} d u

Take the constant out:

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

= 3 \cdot \frac{1}{6} \cdot \int_{2}^{11} e^{u} d u

Use the common integral:

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

= 3 \cdot \frac{1}{6} [e^{u}]_{2}^{11}

Simplify

3 \cdot \frac{1}{6} [e^{u}]_{2}^{11} : \frac{1}{2} [e^{u}]_{2}^{11}

= \frac{1}{2} [e^{u}]_{2}^{11}

Compute the boundaries:

e^{11} - e^{2}

= \frac{1}{2} (e^{11} - e^{2})

Simplify

= \frac{e ^{11} - e ^{2}}{2}

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What is the integral from 1 to 2 of 3xe^{3x^2-1} ?
The integral from 1 to 2 of 3xe^{3x^2-1} is (e^{11}-e^2)/2