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Popular >

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

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x \to 0.01 lim (\frac{e ^{x} - 1}{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