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

The integral from-infinity to 0 of xe^{5x+2} is -(e^2)/(25)

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integral from-infinity to 0 of xe^{5x+2}

\int_{- \infty}^{0} x e^{5 x + 2} d x

- \frac{e ^{2}}{25}

Decimal

- 0.29556 \dots

Solution steps

\int_{- \infty}^{0} x e^{5 x + 2} d x

Compute the indefinite integral:

\int x e^{5 x + 2} d x = \frac{1}{5} e^{5 x + 2} x - \frac{1}{25} e^{5 x + 2} + C

Compute the boundaries:

\int_{- \infty}^{0} x e^{5 x + 2} d x = - \frac{e ^{2}}{25} - 0

= - \frac{e ^{2}}{25} - 0

Simplify

= - \frac{e ^{2}}{25}

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\int_{1}^{3} \frac{x ^{2} + 2}{x} d x

\int_{1}^{2} x + \frac{1}{x ^{2}} d x

What is the integral from-infinity to 0 of xe^{5x+2} ?
The integral from-infinity to 0 of xe^{5x+2} is -(e^2)/(25)