What is the integral from 1 to sqrt(2 of)xe^{5x^2} ?

The integral from 1 to sqrt(2 of)xe^{5x^2} is (e^{10}-e^5)/(10)

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integral from 1 to sqrt(2 of)xe^{5x^2}

\int_{1}^{2} x e^{5 x^{2}} d x

\frac{e ^{10} - e ^{5}}{10}

Decimal

2187.80526 \dots

Solution steps

\int_{1}^{2} x e^{5 x^{2}} d x

Apply u-substitution

: \int_{5}^{10} \frac{e ^{u}}{10} d u

= \int_{5}^{10} \frac{e ^{u}}{10} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int_{5}^{10} e^{u} d u

Use the common integral:

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

= \frac{1}{10} [e^{u}]_{5}^{10}

Compute the boundaries:

e^{10} - e^{5}

= \frac{1}{10} (e^{10} - e^{5})

Simplify

= \frac{e ^{10} - e ^{5}}{10}

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What is the integral from 1 to sqrt(2 of)xe^{5x^2} ?
The integral from 1 to sqrt(2 of)xe^{5x^2} is (e^{10}-e^5)/(10)