What is the integral from-infinity to 15 of xe^{x/5} ?

The integral from-infinity to 15 of xe^{x/5} is 50e^3

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integral from-infinity to 15 of xe^{x/5}

\int_{- \infty}^{15} x e^{\frac{x}{5}} d x

50 e^{3}

Decimal

1004.27684 \dots

Solution steps

\int_{- \infty}^{15} x e^{\frac{x}{5}} d x

Compute the indefinite integral:

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

Compute the boundaries:

\int_{- \infty}^{15} x e^{\frac{x}{5}} d x = 50 e^{3} - 0

= 50 e^{3} - 0

Simplify

= 50 e^{3}

What is the integral from-infinity to 15 of xe^{x/5} ?
The integral from-infinity to 15 of xe^{x/5} is 50e^3