dx-1-x-4-

Question Number 140339 by mohammad17 last updated on 06/May/21

\int \frac{d x}{\sqrt{1 + x^{4}}}

Answered by Dwaipayan Shikari last updated on 06/May/21

\int \frac{d x}{\sqrt{1 + x^{4}}} = \sum_{n ⩾ 0} \int \frac{{(\frac{1}{2})}_{n}}{n!} {(- x^{4})}^{n}

= x \sum_{n ⩾ 0} \frac{{(\frac{1}{2})}_{n} {(\frac{1}{4})}_{n}}{n! {(\frac{5}{4})}_{n}} {(- x^{4})}^{n} = x_{2} F_{1} (\frac{1}{2}, \frac{1}{4}, \frac{5}{4}; - x^{4}) + C