O integrala dificila totusi:
Inainte de a incepe trebuie remarcat faptul ca domeniul maxim e intervalul (2,5).
Avem
^3}dx=-1/2\int\frac{-7+7-2x}{(\sqrt{7x-10-x^2})^3}dx=7/2\int\frac{1}{(\sqrt{7x-10-x^2})^3}dx+(-1/2)\int\frac{(7x-10-x^2)'}{(\sqrt{7x-10-x^2})^3}dx=(7x-10-x^2)^{-1/2}+7/2\int\frac{dx}{(\sqrt{(9/4-(x-7/2)^2)})^3)
Separat rezolvam
^2)})^3)
Se face substitutia x-7/2=9/4siny avem dx=9/4cosydy si integrala devine:
etc
Edit:Am gresit la substitutie in loc de x-7/2=9/4siny vine x-7/2=3/2siny.Asta nu schimba foarte mult ideea de rezolvare.
