Интеграл dx/(1+x^4) (dx)

$$int_{0}^{1} frac{1}{x^{4} + 1}, dx$$

1
/
| ___ / ___ ___ ___ / ___
| 1 / 2 *log2 – / 2 / pi*/ 2 / 2 *log2 + / 2 /
| —— dx = – ——————– + ——– + ——————–
| 4 8 8 8
| 1 + x
|
/
0

$${{log left(sqrt{2}+2right)}over{2^{{{5}over{2}}}}}-{{log
left(2-sqrt{2}right)}over{2^{{{5}over{2}}}}}+{{pi}over{2^{{{5
}over{2}}}}}$$

0.866972987339911

/
| ___ / 2 ___ ___ / ___ ___ / ___ ___ / 2 ___
| 1 / 2 *log1 + x – x*/ 2 / / 2 *atan1 + x*/ 2 / / 2 *atan -1 + x*/ 2 / / 2 *log1 + x + x*/ 2 /
| —— dx = C – ————————— + ———————– + ———————— + —————————
| 4 8 4 4 8
| 1 + x
|
/

$${{log left(x^2+sqrt{2},x+1right)}over{2^{{{5}over{2}}}}}-{{
log left(x^2-sqrt{2},x+1right)}over{2^{{{5}over{2}}}}}+{{
arctan left({{2,x+sqrt{2}}over{sqrt{2}}}right)}over{2^{{{3
}over{2}}}}}+{{arctan left({{2,x-sqrt{2}}over{sqrt{2}}}
right)}over{2^{{{3}over{2}}}}}$$

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