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[tex] \int\limit \frac{ x^{2} -x-2}{x-2} dx[/tex]

Răspuns :

[tex] \int\limits { \frac{ x^{2} -x-2}{x-2} } \, dx = \int\limits { \frac{ x^{2} -2x+x-2}{x-2} } \, dx = \int\limits{ \frac{ x^{2} -2x}{x-2} } \, dx + \int\limits { \frac{x-2}{x-2} } \, dx [/tex]
[tex]= \int\limits {x} \, dx + \int\limits\, dx = \frac{ x^{2} }{2} +x[/tex]
Red12dog34ask
[tex]x^2-x-2=(x+1)(x-2)[/tex].
Deci
 [tex]\displaystyle\int\frac{x^2-x-2}{x-2}dx=\int\frac{(x+1)(x-2)}{x-2}dx=\\=\displaystyle\int (x+1)dx=\frac{x^2}{2}+x+C[/tex]

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