Odpowiedź:
[tex]t=\sqrt{x}[/tex]
[tex]dt = \frac{1}{2\sqrt{x}}dx[/tex]
[tex]dx = 2\sqrt{x}dt[/tex]
[tex]\int \frac{\sqrt{x}}{x+1}dx = \int (\frac{t}{x+1} 2\sqrt{x})dt = \int \frac{2t^2}{t^2+1}dt = 2\int \frac{t^2}{t^2 + 1}dt = 2\int (1 - \frac{1}{t^2+1})dt = 2(\int 1dt - \int \frac{1}{t^2+1}dt) = 2(t - arctan(t)) = 2(\sqrt{x} - arctan(\sqrt{x})) + C[/tex]
