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

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

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integral from 1 to infinity of 1/(5^x)

\int_{1}^{\infty} \frac{1}{5 ^{x}} d x

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

Decimal

0.12426 \dots

Solution steps

\int_{1}^{\infty} \frac{1}{5 ^{x}} d x

Compute the indefinite integral:

\int \frac{1}{5 ^{x}} d x = - \frac{1}{ln ( 5 ) \cdot 5 ^{x}} + C

Compute the boundaries:

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

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

Simplify

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

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