What is the integral from-infinity to 0 of 8^r ?

The integral from-infinity to 0 of 8^r is 1/(3ln(2))

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integral from-infinity to 0 of 8^r

\int_{- \infty}^{0} 8^{r} d r

\frac{1}{3 ln ( 2 )}

Decimal

0.48089 \dots

Solution steps

\int_{- \infty}^{0} 8^{r} d r

Compute the indefinite integral:

\int 8^{r} d r = \frac{8 ^{r}}{3 ln ( 2 )} + C

Compute the boundaries:

\int_{- \infty}^{0} 8^{r} d r = \frac{1}{3 ln ( 2 )} - 0

= \frac{1}{3 ln ( 2 )} - 0

Simplify

= \frac{1}{3 ln ( 2 )}

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What is the integral from-infinity to 0 of 8^r ?
The integral from-infinity to 0 of 8^r is 1/(3ln(2))