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

The integral from-infinity to 0 of z/(z^4+4) is -pi/8

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

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

- \frac{π}{8}

Decimal

- 0.39269 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

\int_{- \infty}^{0} \frac{z}{z ^{4} + 4} d z = 0 - \frac{π}{8}

= 0 - \frac{π}{8}

Simplify

= - \frac{π}{8}

What is the integral from-infinity to 0 of z/(z^4+4) ?
The integral from-infinity to 0 of z/(z^4+4) is -pi/8