en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5-e^{-x}

Solution

\int 5 - e^{- x} d x

Solution

5 x + e^{- x} + C

Solution steps

\int 5 - e^{- x} d x

Apply u-substitution

: \int - 5 + e^{u} d u

= \int - 5 + e^{u} d u

Apply the Sum Rule:

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

= - \int 5 d u + \int e^{u} d u

\int 5 d u = 5 u

\int e^{u} d u = e^{u}

= - 5 u + e^{u}

Substitute back

u = - x

= - 5 (- x) + e^{- x}

Simplify

= 5 x + e^{- x}

Add a constant to the solution

= 5 x + e^{- x} + C

Graph

Popular Examples

integral of 1/(sqrt(z^2+x^2))

\int \frac{1}{z ^{2} + x ^{2}} d x

integral of (e^{3/t})/(t^2)

\int \frac{e ^{\frac{3}{t}}}{t ^{2}} d t

integral of cos(x)x^3

\int cos (x) x^{3} d x

integral of (log_{2}(x))^2

\int (lo g_{2} (x))^{2} d x

integral of e^xsqrt(36+e^x)

\int e^{x} 36 + e^{x} d x

Frequently Asked Questions (FAQ)

What is the integral of 5-e^{-x} ?
The integral of 5-e^{-x} is 5x+e^{-x}+C