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

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

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

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

- \frac{π}{8}

Decimal Notation

- 0.39269 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - \frac{π}{8}

Simplify

= - \frac{π}{8}

\int \frac{2}{4 x ^{2} + 4} d x

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f (x) = 3^{x}, at x = 0

\int - 9 sin (3 t) d t

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