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

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

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

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

\frac{1}{ln ( 3 )}

Decimal Notation

0.91023 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

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

Simplify

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

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