What is the integral from 0 to infinity of x/(x^4+3) ?

The integral from 0 to infinity of x/(x^4+3) is pi/(4sqrt(3))

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integral from 0 to infinity of x/(x^4+3)

\int_{0}^{\infty} \frac{x}{x ^{4} + 3} d x

\frac{π}{4 3}

Decimal

0.45344 \dots

Solution steps

\int_{0}^{\infty} \frac{x}{x ^{4} + 3} d x

Compute the indefinite integral:

\int \frac{x}{x ^{4} + 3} d x = \frac{1}{2 3} arctan (\frac{x ^{2}}{3}) + C

Compute the boundaries:

\int_{0}^{\infty} \frac{x}{x ^{4} + 3} d x = \frac{π}{4 3} - 0

= \frac{π}{4 3} - 0

Simplify

= \frac{π}{4 3}

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What is the integral from 0 to infinity of x/(x^4+3) ?
The integral from 0 to infinity of x/(x^4+3) is pi/(4sqrt(3))