en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/x+2

Solution

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

Solution

ln ∣ x ∣ + 2 x + C

Solution steps

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

\int \frac{1}{x} d x = ln ∣ x ∣

\int 2 d x = 2 x

= ln ∣ x ∣ + 2 x

Add a constant to the solution

= ln ∣ x ∣ + 2 x + C

Graph

Popular Examples

integral of (x^3)/(\sqrt[9]{x^2+7)}

\int \frac{x ^{3}}{9 x ^{2} + 7} d x

derivative of sqrt(x)e^x derivative of

x e^{x}

derivative of e^{x^2*\sqrt[3]{4x-1}}

\frac{d}{d x} (e^{x^{2} \cdot 3 4 x - 1})

integral of (2x+1)/(2x)

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

integral of (6x^4-5x^3+4x^2)/(2x^2-x+1)

\int \frac{6 x ^{4} - 5 x ^{3} + 4 x ^{2}}{2 x ^{2} - x + 1} d x

Frequently Asked Questions (FAQ)

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