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

$$\mathrm{Find}:$$$$\mathbf{\Omega }=\int \frac{{\mathrm{x}}^7-{\mathrm{x}}^5+{\mathrm{x}}^3-\mathrm{x}}{1+{\mathrm{x}}^{10}}\mathrm{dx};\mathrm{x}\in \mathbb{R}$$

Commented by tabata last updated on 15/Oct/21

$$\mathbf{\Omega }=\int \frac{{\mathit{x}}^7-{\mathit{x}}^5+{\mathit{x}}^3-\mathit{x}}{1+{\mathit{x}}^{10}}\mathit{d}\mathit{x}$$$$$$$$\mathbf{\Omega }=\int (-\frac{2}{5})\frac{2\mathit{x}}{({\mathit{x}}^2+1)}+\frac{4{\mathit{x}}^7-3{\mathit{x}}^5+2{\mathit{x}}^3-\mathit{x}}{5({\mathit{x}}^8-{\mathit{x}}^6+{\mathit{x}}^4-{\mathit{x}}^2+1)}\mathit{d}\mathit{x}$$$$$$$$\mathbf{\Omega }=-\frac{2}{5}\mathit{l}\mathit{n}\mid {\mathit{x}}^2+1\mid +\frac{1}{10}\mathit{l}\mathit{n}\mid {\mathit{x}}^8-{\mathit{x}}^6+{\mathit{x}}^4-{\mathit{x}}^2+1\mid +\mathit{C}$$$$$$$$⟨\mathit{M}.\mathit{T}⟩$$

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