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

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

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

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

- \frac{π}{4}

Solution steps

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

= 0 - \frac{π}{4}

Simplify

= - \frac{π}{4}

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