What is the integral from 1 to infinity of 5^{-x} ?

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

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integral from 1 to infinity of 5^{-x}

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

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

Decimal

0.12426 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

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

Simplify

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

x \to 1 lim (e^{6 x^{3} - 6 x})

\frac{\partial}{\partial x} (2 ln (y^{3} + x^{2}))

x^{2} - x - 2, 3

x \to - 10 lim (2 x - 10)

\int_{0}^{6} 6 t - 2 t^{2} d t

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