What is the integral from-infinity to 0 of (xe^{2x}) ?

The integral from-infinity to 0 of (xe^{2x}) is -1/4

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integral from-infinity to 0 of (xe^{2x})

\int_{- \infty}^{0} (x e^{2 x}) d x

- \frac{1}{4}

Decimal

- 0.25

Solution steps

\int_{- \infty}^{0} x e^{2 x} d x

Compute the indefinite integral:

\int x e^{2 x} d x = \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x}) + C

Compute the boundaries:

\int_{- \infty}^{0} (x e^{2 x}) d x = - \frac{1}{4} - 0

= - \frac{1}{4} - 0

Simplify

= - \frac{1}{4}

What is the integral from-infinity to 0 of (xe^{2x}) ?
The integral from-infinity to 0 of (xe^{2x}) is -1/4