What is the integral from-infinity to 0 of 5^x ?

The integral from-infinity to 0 of 5^x is 1/(ln(5))

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integral from-infinity to 0 of 5^x

\int_{- \infty}^{0} 5^{x} d x

\frac{1}{ln ( 5 )}

Decimal

0.62133 \dots

Solution steps

\int_{- \infty}^{0} 5^{x} d x

Compute the indefinite integral:

\int 5^{x} d x = \frac{5 ^{x}}{ln ( 5 )} + C

Compute the boundaries:

\int_{- \infty}^{0} 5^{x} d x = \frac{1}{ln ( 5 )} - 0

= \frac{1}{ln ( 5 )} - 0

Simplify

= \frac{1}{ln ( 5 )}

What is the integral from-infinity to 0 of 5^x ?
The integral from-infinity to 0 of 5^x is 1/(ln(5))