What is the integral of (8e^2x)-(3e^{-x}) ?

The integral of (8e^2x)-(3e^{-x}) is 4e^2x^2+3e^{-x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (8e^2x)-(3e^{-x})

\int (8 e^{2} x) - (3 e^{- x}) d x

4 e^{2} x^{2} + 3 e^{- x} + C

Solution steps

\int 8 e^{2} x - 3 e^{- 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 8 e^{2} x d x - \int 3 e^{- x} d x

\int 8 e^{2} x d x = 4 e^{2} x^{2}

\int 3 e^{- x} d x = - 3 e^{- x}

= 4 e^{2} x^{2} - (- 3 e^{- x})

Simplify

= 4 e^{2} x^{2} + 3 e^{- x}

Add a constant to the solution

= 4 e^{2} x^{2} + 3 e^{- x} + C

\frac{d}{d x} ((2 - 2 x)^{2} (3 x + 1)^{2})

\frac{d}{d x} (\frac{a + b x}{c + d x})

3 t e^{- 2 t}

\frac{d}{d x} (3 (x - 1)^{2})

\int \frac{1}{sin ^{4} ( x )} d x

What is the integral of (8e^2x)-(3e^{-x}) ?
The integral of (8e^2x)-(3e^{-x}) is 4e^2x^2+3e^{-x}+C