en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x+1/x)

Solution

\int (x + \frac{1}{x}) d x

Solution

\frac{x ^{2}}{2} + ln ∣ x ∣ + C

Solution steps

\int x + \frac{1}{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 x d x + \int \frac{1}{x} d x

\int x d x = \frac{x ^{2}}{2}

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{x ^{2}}{2} + ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{2}}{2} + ln ∣ x ∣ + C

Popular Examples

(df)/(dx)=tan^3(x)-sec^3(x)

\frac{df}{d x} = tan^{3} (x) - sec^{3} (x)

slope ofintercept (-1,-1),(1,0)slope intercept

(- 1, - 1), (1, 0)

derivative of 2x+xln(x)

\frac{d}{d x} (2 x + x ln (x))

derivative of f(x)=sin(6x)derivative of

f (x) = sin (6 x)

integral from 0 to 1 of x^4

\int_{0}^{1} x^{4} d x

Frequently Asked Questions (FAQ)

What is the integral of (x+1/x) ?
The integral of (x+1/x) is (x^2)/2+ln|x|+C