What is the integral from-infinity to 0 of 13^x ?

The integral from-infinity to 0 of 13^x is 1/(ln(13))

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integral from-infinity to 0 of 13^x

\int_{- \infty}^{0} 1 3^{x} d x

\frac{1}{ln ( 13 )}

Decimal Notation

0.38987 \dots

Solution steps

\int_{- \infty}^{0} 1 3^{x} d x

Compute the indefinite integral:

\int 1 3^{x} d x = \frac{1 3 ^{x}}{ln ( 13 )} + C

Compute the boundaries:

\int_{- \infty}^{0} 1 3^{x} d x = \frac{1}{ln ( 13 )} - 0

= \frac{1}{ln ( 13 )} - 0

Simplify

= \frac{1}{ln ( 13 )}

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What is the integral from-infinity to 0 of 13^x ?
The integral from-infinity to 0 of 13^x is 1/(ln(13))