en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of 5/x-3e^x

Solution

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

Solution

5 ln ∣ x ∣ - 3 e^{x} + C

Solution steps

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

\int \frac{5}{x} d x = 5 ln ∣ x ∣

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

= 5 ln ∣ x ∣ - 3 e^{x}

Add a constant to the solution

= 5 ln ∣ x ∣ - 3 e^{x} + C

Graph

Popular Examples

integral of 8/x-9e^x

integral of 3cos(3x-1)

integral of (tanh(x))

integral of e^{(x^2-1)}

integral of (x^3)/(7-5x^4)

Frequently Asked Questions (FAQ)

What is the integral of 5/x-3e^x ?
The integral of 5/x-3e^x is 5ln|x|-3e^x+C