What is the integral of (2x)/5+2/x ?

The integral of (2x)/5+2/x is (x^2)/5+2ln|x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{x ^{2}}{5} + 2 ln ∣ x ∣ + C

Solution steps

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

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= \frac{x ^{2}}{5} + 2 ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{2}}{5} + 2 ln ∣ x ∣ + C

\int - 6 x^{2} 2^{4 x} d x

\int [12 + csc (x) (sin (x) + csc (x))] d x

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

\int (1 - x)^{6} d x

\int \frac{t ^{2}}{t ^{2} + 4} d t

What is the integral of (2x)/5+2/x ?
The integral of (2x)/5+2/x is (x^2)/5+2ln|x|+C