What is the integral from 1 to infinity of 1/(6^x) ?

The integral from 1 to infinity of 1/(6^x) is 1/(6ln(6))

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integral from 1 to infinity of 1/(6^x)

\int_{1}^{\infty} \frac{1}{6 ^{x}} d x

\frac{1}{6 ln ( 6 )}

Decimal Notation

0.09301 \dots

Solution steps

\int_{1}^{\infty} \frac{1}{6 ^{x}} d x

Compute the indefinite integral:

\int \frac{1}{6 ^{x}} d x = - \frac{1}{ln ( 6 ) \cdot 6 ^{x}} + C

Compute the boundaries:

\int_{1}^{\infty} \frac{1}{6 ^{x}} d x = 0 - (- \frac{1}{6 ln ( 6 )})

= 0 - (- \frac{1}{6 ln ( 6 )})

Simplify

= \frac{1}{6 ln ( 6 )}

\int_{\frac{- π}{2}}^{\frac{π}{2}} 1 d x

\int_{0}^{4} 2 + 6 x d x

\int_{0}^{4} \frac{x}{3} d x

\int_{- 3}^{2} \frac{6}{x ^{3}} d x

\int_{8}^{3} 1 d x

What is the integral from 1 to infinity of 1/(6^x) ?
The integral from 1 to infinity of 1/(6^x) is 1/(6ln(6))