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Cum se rezolva urmatoarea integrala: [tex] \int\ {\frac{1}{x^3+x^5}} \, dx [/tex]

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[tex]\int \frac{1}{x^3+x^5}dx \\ =\int \frac{1}{x^3}+\frac{x}{x^2+1}-\frac{1}{x}dx \\ \int \frac{1}{x^3}dx+\int \frac{x}{x^2+1}dx-\int \frac{1}{x}dx \\ Calculam : \int \frac{1}{x^3}dx=-\frac{1}{2x^2} \\ \int \frac{x}{x^2+1}dx=\frac{1}{2}\ln \left|x^2+1\right| \\ \int \frac{x}{x^2+1}dx=\frac{1}{2}\ln \left|x^2+1\right| \\ Deci : \int \frac{1}{x^3}dx+\int \frac{x}{x^2+1}dx-\int \frac{1}{x}dx[/tex][tex]=-\frac{1}{2x^2}+\frac{1}{2}\ln \left|x^2+1\right|-\ln \left|x\right|=-\frac{1}{2x^2}+\frac{1}{2}\ln \left|x^2+1\right|-\ln \left|x\right|+C[/tex]

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