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

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

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

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

- \frac{π}{8}

Decimal

- 0.39269 \dots

Solution steps

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

= \frac{π}{8} - \frac{π}{4}

Simplify

= - \frac{π}{8}

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