BeMath-x-5-x-x-8-1-dx-

Question Number 108169 by bemath last updated on 15/Aug/20

\frac{✓ B e M a t h ✓}{≻≺}

\int \frac{x^{5} - x}{x^{8} - 1} d x ?

Answered by Dwaipayan Shikari last updated on 15/Aug/20

\int \frac{x (x^{4} - 1)}{(x^{8} - 1)} d x

\int \frac{x}{x^{4} + 1} d x x^{2} = u, 2 x = \frac{d u}{d x}

\frac{1}{2} \int \frac{d u}{u^{2} + 1} = \frac{1}{2} {t a n}^{- 1} u + C = \frac{1}{2} {t a n}^{- 1} (x^{2}) + C