What is the integral from 0 to 1 of (x/(1+x^4)) ?

The integral from 0 to 1 of (x/(1+x^4)) is pi/8

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 1 of (x/(1+x^4))

\int_{0}^{1} (\frac{x}{1 + x ^{4}}) d x

\frac{π}{8}

Decimal Notation

0.39269 \dots

Solution steps

\int_{0}^{1} \frac{x}{1 + x ^{4}} d x

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{1} (\frac{x}{1 + x ^{4}}) d x = \frac{π}{8} - 0

= \frac{π}{8} - 0

Simplify

= \frac{π}{8}

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

\int_{1}^{3} \frac{x + 3}{x ^{2} + 6 x} d x

\int_{4}^{\infty} \frac{6}{x ^{4}} d x

\int_{0}^{1} (\frac{y}{e ^{2 y}}) d y

\int_{1}^{5} \frac{cos ( x )}{x} d x

What is the integral from 0 to 1 of (x/(1+x^4)) ?
The integral from 0 to 1 of (x/(1+x^4)) is pi/8