Question

Cat face integrala din x patrat supra x+1 dx?

Answer 1

$\int\frac{x^2}{x+1}dx=\int\frac{x^2+x-x}{x+1}dx= \\ \\ =\int\frac{x^2+x}{x+1}dx-\int\frac{x}{x+1}dx= \\ \\ =\int\frac{x(x+1)}{x+1}dx-\int\frac{x+1-1}{x+1}dx= \\ \\ =\int x dx-\int\frac{x+1}{x+1}dx-\int\frac{-1}{x+1}dx= \\ \\ =\int xdx-\int 1 dx+\int\frac{1}{x+1}dx= \\ \\ =\frac{x^2}{2}-x+\ln (x+1)$

+CONSTANTA, bineînțeles.