Find-x-7-x-5-x-3-x-1-x-10-dx-x-R-

Question Number 156808 by MathSh last updated on 15/Oct/21

Find :

Ω = \int \frac{x^{7} - x^{5} + x^{3} - x}{1 + x^{10}} dx; x \in R

Commented by tabata last updated on 15/Oct/21

Ω = \int \frac{x^{7} - x^{5} + x^{3} - x}{1 + x^{10}} d x

Ω = \int (- \frac{2}{5}) \frac{2 x}{(x^{2} + 1)} + \frac{4 x^{7} - 3 x^{5} + 2 x^{3} - x}{5 (x^{8} - x^{6} + x^{4} - x^{2} + 1)} d x

Ω = - \frac{2}{5} l n ∣ x^{2} + 1 ∣ + \frac{1}{10} l n ∣ x^{8} - x^{6} + x^{4} - x^{2} + 1 ∣ + C

⟨ M . T ⟩

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