find-x-2-dx-x-3-8-x-4-1-

Question Number 68037 by mathmax by abdo last updated on 03/Sep/19

f i n d \int \frac{x^{2} d x}{(x^{3} - 8) (x^{4} + 1)}

Answered by MJS last updated on 04/Sep/19

\int \frac{x^{2}}{(x^{3} - 8) (x^{4} + 1)} d x =

= \frac{1}{51} \int \frac{d x}{x - 2} -

- \frac{14}{723} \int \frac{x - \frac{17}{7}}{x^{2} + 2 x + 4} d x -

- \frac{1 - 252 \sqrt{2}}{8194} \int \frac{x - \frac{8 + \sqrt{2}}{62}}{x^{2} - \sqrt{2} x + 1} d x -

- \frac{1 + 252 \sqrt{2}}{8194} \int \frac{x - \frac{8 - \sqrt{2}}{62}}{x^{2} + \sqrt{2} x + 1} d x =

= \frac{1}{51} \ln (x - 2) -

- \frac{7}{723} \ln (x^{2} + 2 x + 4) + \frac{16 \sqrt{3}}{723} \arctan \frac{\sqrt{3} (x + 1)}{3} -

- \frac{1 + 252 \sqrt{2}}{16388} \ln (x^{2} - \sqrt{2} x + 1) + \frac{2 (16 - 65 \sqrt{2})}{4097} \arctan (\sqrt{2} x - 1) -

- \frac{1 - 252 \sqrt{2}}{16388} \ln (x^{2} + \sqrt{2} x + 1) - \frac{2 (16 + 65 \sqrt{2})}{4097} \arctan (\sqrt{2} x + 1) + C

Commented by turbo msup by abdo last updated on 04/Sep/19

t h a n k y o u s i r m j s