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

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

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

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

\frac{π}{8}

Decimal Notation

0.39269 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= \frac{π}{8} - 0

Simplify

= \frac{π}{8}

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