JS-dx-x-8-x-2-1-

Question Number 108325 by john santu last updated on 16/Aug/20

\frac{⊸ J S ⊸}{- - - -}

\int \frac{d x}{x^{8} (x^{2} + 1)} = ?

Commented by john santu last updated on 16/Aug/20

\frac{⊸ J S ⊸}{______}

\int \frac{d x}{x^{8} (x^{2} + 1)} = \int (\frac{1}{x^{2} + 1} - \frac{1}{x^{2}} + \frac{1}{x^{4}} - \frac{1}{x^{6}} + \frac{1}{x^{8}}) d x

= \tan^{- 1} (x) + \frac{1}{x} - \frac{1}{3 x^{3}} + \frac{1}{5 x^{5}} - \frac{1}{7 x^{7}} + c