What is the integral from-infinity to 8 of re^{r/2} ?

The integral from-infinity to 8 of re^{r/2} is 12e^4

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integral from-infinity to 8 of re^{r/2}

\int_{- \infty}^{8} r e^{\frac{r}{2}} d r

12 e^{4}

Decimal Notation

655.17780 \dots

Solution steps

\int_{- \infty}^{8} r e^{\frac{r}{2}} d r

Compute the indefinite integral:

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

Compute the boundaries:

\int_{- \infty}^{8} r e^{\frac{r}{2}} d r = 12 e^{4} - 0

= 12 e^{4} - 0

Simplify

= 12 e^{4}

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\int_{- 1}^{1} (x^{2} + 1)^{2} d x

y = e^{- \frac{1}{2} x}

(2 x^{3} + 5 x) (x - 3) (x + 2)

What is the integral from-infinity to 8 of re^{r/2} ?
The integral from-infinity to 8 of re^{r/2} is 12e^4