[tex]\displaystyle\int\left(\dfrac{1-x}{x^2}\right)^2dx=\displaystyle\int\left(\dfrac{1}{x^2}-\dfrac1x\right)^2dx=\displaystyle\int\left(\dfrac{1}{x^4}-\dfrac{2}{x^3}+\dfrac{1}{x^2}\right)dx=[/tex]
[tex]\displaystyle\int\left(x^{-4}-2x^{-3}+x^{-2})dx=\dfrac{x^{-3}}{-3}-2\cdot\dfrac{x^{-2}}{-2}+\dfrac{x^{-1}}{-1}+C=[/tex]
[tex]=-\dfrac{1}{3x^3}+\dfrac{1}{x^2}-\dfrac1x+C[/tex]
Dupa a doua egalitate am folosit formula [tex](A-B)^2=A^2-2AB+B^2[/tex]
Am folosit si:
[tex]\int x^ndx=\dfrac{x^{n+1}}{n+1}+C[/tex]
Am folosit si :
[tex]x^{-n}=\dfrac{1}{x^n} [/tex]
