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

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

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

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

\frac{π}{4}

Decimal Notation

0.78539 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{1} \frac{2 x}{1 + x ^{4}} d x = \frac{π}{4} - 0

= \frac{π}{4} - 0

Simplify

= \frac{π}{4}

f (x) = \frac{- 4 x}{x ^{2} + 1}, at x = 0

x \to 3 lim (\frac{x ^{2} - 6}{x - 3})

\frac{d ^{2}}{d x ^{2}} (\frac{2}{3 t ^{4}})

ln (1 + 2 \cdot t), 2

\frac{d}{d x} (\frac{4 x - 1}{x ^{2}})

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