What is the integral from 0 to 2 of (x/(1+x^4)) ?

The integral from 0 to 2 of (x/(1+x^4)) is 1/2 arctan(4)

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integral from 0 to 2 of (x/(1+x^4))

\int_{0}^{2} (\frac{x}{1 + x ^{4}}) d x

\frac{1}{2} arctan (4)

Decimal

0.66290 \dots

Solution steps

\int_{0}^{2} \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}^{2} (\frac{x}{1 + x ^{4}}) d x = \frac{1}{2} arctan (4) - 0

= \frac{1}{2} arctan (4) - 0

Simplify

= \frac{1}{2} arctan (4)

What is the integral from 0 to 2 of (x/(1+x^4)) ?
The integral from 0 to 2 of (x/(1+x^4)) is 1/2 arctan(4)