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

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

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

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

\frac{π}{4}

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= \frac{π}{4} - 0

Simplify

= \frac{π}{4}

\int e^{\frac{2 x}{π}} d x

\int \frac{( x + 1 )}{x ^{2} + 5 x + 6} d x

1 - 3 x

\int \frac{tan ( ln ( 2 x + 4 ) )}{2 x + 4} d x

4 x + 1

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