What is the integral of 4/(x^2+1) ?

The integral of 4/(x^2+1) is 4arctan(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 4/(x^2+1)

\int \frac{4}{x ^{2} + 1} d x

4 arctan (x) + C

Solution steps

\int \frac{4}{x ^{2} + 1} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int \frac{1}{x ^{2} + 1} d x

Use the common integral:

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

= 4 arctan (x)

Add a constant to the solution

= 4 arctan (x) + C

\int (3 x^{2} + 1)^{3} x d x

x \to - 1 lim (\frac{x}{x ^{2} + 1})

\int_{0}^{6} 2 x + 1 d x

x \to 0 lim (sin (x) \cdot \frac{1}{x})

\frac{d}{d x} ((\frac{2 x}{x + 2})^{4})