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

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

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integral from-infinity to 0 of x^2e^{2x}

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

\frac{1}{4}

Decimal

0.25

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= \frac{1}{4} - 0

Simplify

= \frac{1}{4}

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