en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of 4-2^{-x}

Solution

\int 4 - 2^{- x} d x

Solution

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

Solution steps

\int 4 - 2^{- x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 4 d x - \int 2^{- x} d x

\int 4 d x = 4 x

\int 2^{- x} d x = - \frac{2 ^{- x}}{ln ( 2 )}

= 4 x - (- \frac{2 ^{- x}}{ln ( 2 )})

Simplify

= 4 x + \frac{2 ^{- x}}{ln ( 2 )}

Add a constant to the solution

= 4 x + \frac{2 ^{- x}}{ln ( 2 )} + C

Graph

Popular Examples

integral of x^{22}

integral of (e^x+1/(e^{2x)})^2

integral of (x-5)/(x^2(x+1))

integral of 1/(3+4cos^2(x))

integral of-(x-2)^2

Frequently Asked Questions (FAQ)

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