What is the integral from 0 to 5 of 4xe^{2x^2} ?

The integral from 0 to 5 of 4xe^{2x^2} is e^{50}-1

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integral from 0 to 5 of 4xe^{2x^2}

\int_{0}^{5} 4 x e^{2 x^{2}} d x

e^{50} - 1

Decimal

5.18471 E 21

Solution steps

\int_{0}^{5} 4 x e^{2 x^{2}} d x

Take the constant out:

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

= 4 \cdot \int_{0}^{5} x e^{2 x^{2}} d x

Apply u-substitution

: \int_{0}^{50} \frac{e ^{u}}{4} d u

= 4 \cdot \int_{0}^{50} \frac{e ^{u}}{4} d u

Take the constant out:

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

= 4 \cdot \frac{1}{4} \cdot \int_{0}^{50} e^{u} d u

Use the common integral:

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

= 4 \cdot \frac{1}{4} [e^{u}]_{0}^{50}

Simplify

4 \cdot \frac{1}{4} [e^{u}]_{0}^{50} : [e^{u}]_{0}^{50}

= [e^{u}]_{0}^{50}

Compute the boundaries:

e^{50} - 1

= e^{50} - 1

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What is the integral from 0 to 5 of 4xe^{2x^2} ?
The integral from 0 to 5 of 4xe^{2x^2} is e^{50}-1