What is the integral of (4e^{-2x}+5e^{3x}) ?

The integral of (4e^{-2x}+5e^{3x}) is -2e^{-2x}+5/3 e^{3x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (4e^{-2x}+5e^{3x})

\int (4 e^{- 2 x} + 5 e^{3 x}) d x

- 2 e^{- 2 x} + \frac{5}{3} e^{3 x} + C

Solution steps

\int 4 e^{- 2 x} + 5 e^{3 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 e^{- 2 x} d x + \int 5 e^{3 x} d x

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

\int 5 e^{3 x} d x = \frac{5}{3} e^{3 x}

= - 2 e^{- 2 x} + \frac{5}{3} e^{3 x}

Add a constant to the solution

= - 2 e^{- 2 x} + \frac{5}{3} e^{3 x} + C

\int \frac{( sin ( x ) - cos ( x ) )}{sin ( x )} d x

\int \frac{1}{e ^{2 x} + 4 e ^{x}} d x

\int sin (3 y) ln (x)

\int \frac{9 x}{x ^{3} - 3 x + 2} d x

\int \frac{1}{- x ^{2} + 10 x - 16} d x

What is the integral of (4e^{-2x}+5e^{3x}) ?
The integral of (4e^{-2x}+5e^{3x}) is -2e^{-2x}+5/3 e^{3x}+C