What is the integral from-infinity to 9 of re^{r/3} ?

The integral from-infinity to 9 of re^{r/3} is 18e^3

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integral from-infinity to 9 of re^{r/3}

\int_{- \infty}^{9} r e^{\frac{r}{3}} d r

18 e^{3}

Decimal Notation

361.53966 \dots

Solution steps

\int_{- \infty}^{9} r e^{\frac{r}{3}} d r

Compute the indefinite integral:

\int r e^{\frac{r}{3}} d r = 3 e^{\frac{r}{3}} r - 9 e^{\frac{r}{3}} + C

Compute the boundaries:

\int_{- \infty}^{9} r e^{\frac{r}{3}} d r = 18 e^{3} - 0

= 18 e^{3} - 0

Simplify

= 18 e^{3}

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What is the integral from-infinity to 9 of re^{r/3} ?
The integral from-infinity to 9 of re^{r/3} is 18e^3