What is the integral from 0 to infinity of x/(3+x^4) ?

The integral from 0 to infinity of x/(3+x^4) is pi/(4sqrt(3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to infinity of x/(3+x^4)

\int_{0}^{\infty} \frac{x}{3 + x ^{4}} d x

\frac{π}{4 3}

Decimal

0.45344 \dots

Solution steps

\int_{0}^{\infty} \frac{x}{3 + x ^{4}} d x

Compute the indefinite integral:

\int \frac{x}{3 + x ^{4}} d x = \frac{1}{2 3} arctan (\frac{x ^{2}}{3}) + C

Compute the boundaries:

\int_{0}^{\infty} \frac{x}{3 + x ^{4}} d x = \frac{π}{4 3} - 0

= \frac{π}{4 3} - 0

Simplify

= \frac{π}{4 3}

What is the integral from 0 to infinity of x/(3+x^4) ?
The integral from 0 to infinity of x/(3+x^4) is pi/(4sqrt(3))