What is the integral of x/(x^3+x) ?

The integral of x/(x^3+x) is arctan(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x/(x^3+x)

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

arctan (x) + C

Solution steps

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

Simplify

\frac{x}{x ^{3} + x} : \frac{1}{x ^{2} + 1}

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

Use the common integral:

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

= arctan (x)

Add a constant to the solution

= arctan (x) + C

n = 0 \sum \infty 2^{- \frac{n}{2}}

y = ln (5 x^{2} + 3 y^{2})

x \to 4 + lim (\frac{2 x}{x - 4})

\int \frac{tan ^{3} ( \frac{7}{z} )}{z ^{2}} d z

\frac{\partial}{\partial z} (x e^{2 yz})