en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (1/2)^x

Solution

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

Popular Examples

limit as x approaches 1+of 8/(sqrt(1-x))

x \to 1 + lim (\frac{8}{1 - x})

derivative of (6x^2+6x+4/(sqrt(x)))

\frac{d}{d x} (\frac{6 x ^{2} + 6 x + 4}{x})

integral of 4/(x-1)

\int \frac{4}{x - 1} d x

inverse oflaplace (6s-4)/(s^2-4s+20)inverse laplace

\frac{6 s - 4}{s ^{2} - 4 s + 20}

limit as x approaches 0 of xcos(1/(x^3))

x \to 0 lim (x cos (\frac{1}{x ^{3}}))

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