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Popular Calculus >

integral of (1/4)^x

Solution

\int (\frac{1}{4})^{x} d x

Solution

- \frac{1}{ln ( 2 ) \cdot 2 ^{2 x + 1}} + C

Solution steps

\int (\frac{1}{4})^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

= \frac{( \frac{1}{4} ) ^{x}}{ln ( \frac{1}{4} )}

Simplify

\frac{( \frac{1}{4} ) ^{x}}{ln ( \frac{1}{4} )} : - \frac{1}{ln ( 2 ) \cdot 2 ^{2 x + 1}}

= - \frac{1}{ln ( 2 ) \cdot 2 ^{2 x + 1}}

Add a constant to the solution

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

Graph

Popular Examples

limit as x approaches-3 of (1-6x)/(3+x)

x \to - 3 lim (\frac{1 - 6 x}{3 + x})

integral from 0 to 1 of (x^2)/(x^3+1)

\int_{0}^{1} \frac{x ^{2}}{x ^{3} + 1} d x

derivative of (sin(1/x x^3)/(ln(x)))

\frac{d}{d x} (\frac{sin ( \frac{1}{x} ) x ^{3}}{ln ( x )})

area 1-x^2,x^6-x+1

a re a 1 - x^{2}, x^{6} - x + 1

limit as x approaches-infinity of x^4+x

x \to - \infty lim (x^{4} + x)

Frequently Asked Questions (FAQ)

What is the integral of (1/4)^x ?
The integral of (1/4)^x is -1/(ln(2)*2^{2x+1)}+C