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Popular >

integral of (1/2)^x

Solution

integral

(\frac{1}{2})^{x}

Solution

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

Solution steps

\int (\frac{1}{2})^{x} d x

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

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

Simplify

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

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

Add a constant to the solution

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

Graph

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Frequently Asked Questions (FAQ)

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