What is the integral from-infinity to 0 of 3^{8x} ?

The integral from-infinity to 0 of 3^{8x} is 1/(8ln(3))

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integral from-infinity to 0 of 3^{8x}

\int_{- \infty}^{0} 3^{8 x} d x

\frac{1}{8 ln ( 3 )}

Decimal

0.11377 \dots

Solution steps

\int_{- \infty}^{0} 3^{8 x} d x

Compute the indefinite integral:

\int 3^{8 x} d x = \frac{656 1 ^{x}}{8 ln ( 3 )} + C

Compute the boundaries:

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

= \frac{1}{8 ln ( 3 )} - 0

Simplify

= \frac{1}{8 ln ( 3 )}

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