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

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

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integral from 0 to infinity of 5^{-x}

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

\frac{1}{ln ( 5 )}

Decimal Notation

0.62133 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

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

Simplify

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

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