en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^x+5/x

Solution

\int e^{x} + \frac{5}{x} d x

Solution

e^{x} + 5 ln ∣ x ∣ + C

Solution steps

\int e^{x} + \frac{5}{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 e^{x} d x + \int \frac{5}{x} d x

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

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= e^{x} + 5 ln ∣ x ∣

Add a constant to the solution

= e^{x} + 5 ln ∣ x ∣ + C

Graph

Popular Examples

integral of 18x+36x^2

\int 18 x + 36 x^{2} d x

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

\int \frac{x}{5 x ^{2} + 2} d x

integral of \sqrt[5]{5-2x}

\int 5 5 - 2 x d x

integral of x(5x^2+8)^{10}

\int x (5 x^{2} + 8)^{10} d x

integral of (12x^3+8x^2-6)/(x^2)

\int \frac{12 x ^{3} + 8 x ^{2} - 6}{x ^{2}} d x

Frequently Asked Questions (FAQ)

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