find-dx-1-x-6-

Question Number 70686 by mathmax by abdo last updated on 06/Oct/19

f i n d \int \frac{d x}{1 + x^{6}}

Answered by kaivan.ahmadi last updated on 06/Oct/19

Answered by MJS last updated on 07/Oct/19

\int \frac{d x}{x^{6} + 1} =

= \frac{1}{3} \int \frac{d x}{x^{2} + 1} + \frac{1}{6} \int \frac{\sqrt{3} x + 2}{x^{2} + \sqrt{3} x + 1} d x - \frac{1}{6} \int \frac{\sqrt{3} x - 2}{x^{2} - \sqrt{3} x + 1} d x =

= \frac{1}{3} \arctan x +

+ \frac{\sqrt{3}}{12} \ln (x^{2} + \sqrt{3} x + 1) + \frac{1}{6} \arctan (2 x + \sqrt{3}) -

- \frac{\sqrt{3}}{12} \ln (x^{2} - \sqrt{3} x + 1) + \frac{1}{6} \arctan (2 x - \sqrt{3}) + C

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