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

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

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

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

\frac{π}{8}

Decimal

0.39269 \dots

Solution steps

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

= \frac{π}{4} - \frac{π}{8}

Simplify

= \frac{π}{8}

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