What is the integral from 1 to sqrt(2 of)xe^{7x^2} ?

The integral from 1 to sqrt(2 of)xe^{7x^2} is (e^{14}-e^7)/(14)

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integral from 1 to sqrt(2 of)xe^{7x^2}

\int_{1}^{2} x e^{7 x^{2}} d x

\frac{e ^{14} - e ^{7}}{14}

Decimal

85821.97507 \dots

Solution steps

\int_{1}^{2} x e^{7 x^{2}} d x

Apply u-substitution

: \int_{7}^{14} \frac{e ^{u}}{14} d u

= \int_{7}^{14} \frac{e ^{u}}{14} d u

Take the constant out:

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

= \frac{1}{14} \cdot \int_{7}^{14} e^{u} d u

Use the common integral:

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

= \frac{1}{14} [e^{u}]_{7}^{14}

Compute the boundaries:

e^{14} - e^{7}

= \frac{1}{14} (e^{14} - e^{7})

Simplify

= \frac{e ^{14} - e ^{7}}{14}

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What is the integral from 1 to sqrt(2 of)xe^{7x^2} ?
The integral from 1 to sqrt(2 of)xe^{7x^2} is (e^{14}-e^7)/(14)