What is the integral of (1-(2x)/(x^2+1)) ?

The integral of (1-(2x)/(x^2+1)) is x-ln|x^2+1|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\int (1 - \frac{2 x}{x ^{2} + 1}) d x

x - ln x^{2} + 1 + C

Solution steps

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

\int 1 d x = x

\int \frac{2 x}{x ^{2} + 1} d x = ln x^{2} + 1

= x - ln x^{2} + 1

Add a constant to the solution

= x - ln x^{2} + 1 + C

\int sin^{3} (\frac{x}{2}) \cdot cos^{5} (\frac{x}{2}) d x

\int x^{3} \frac{1}{x} d x

\int \frac{4}{x ^{2} + 3} d x

\int (x^{\frac{3}{2}} - 2 x^{3} + x) d x

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