What is the integral from 1 to infinity of 1/(4^x) ?

The integral from 1 to infinity of 1/(4^x) is 1/(8ln(2))

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integral from 1 to infinity of 1/(4^x)

\int_{1}^{\infty} \frac{1}{4 ^{x}} d x

\frac{1}{8 ln ( 2 )}

Decimal Notation

0.18033 \dots

Solution steps

\int_{1}^{\infty} \frac{1}{4 ^{x}} d x

Compute the indefinite integral:

\int \frac{1}{4 ^{x}} d x = - \frac{1}{ln ( 2 ) \cdot 2 ^{2 x + 1}} + C

Compute the boundaries:

\int_{1}^{\infty} \frac{1}{4 ^{x}} d x = 0 - (- \frac{1}{8 ln ( 2 )})

= 0 - (- \frac{1}{8 ln ( 2 )})

Simplify

= \frac{1}{8 ln ( 2 )}

\int 3 - 3 x d x

\int x cos (2 x) d x

y = e^{x^{6}}

\frac{d y}{d x} + \frac{1}{3} y = e^{x} y^{4}

\frac{\partial}{\partial y} (ln (y^{2}))

What is the integral from 1 to infinity of 1/(4^x) ?
The integral from 1 to infinity of 1/(4^x) is 1/(8ln(2))