[dispmath]\int\!\frac{\sqrt{x+5}}{\sqrt[3]{x+5}-\sqrt{x+5}}\,\mathrm dx[/dispmath] Prvo sam uveo smenu [inlmath]x+5=t[/inlmath] i dobio:
[dispmath]\int\!\frac{\sqrt t}{\sqrt[3]t-\sqrt t}\,\mathrm dt=\int\!\frac{\sqrt t}{\sqrt t\left(\frac{1}{\sqrt[6]t}-1\right)}\,\mathrm dt=\int\!\frac{\sqrt[6]t}{1-\sqrt[6]t}\,\mathrm dt\\
-\int\!\frac{\sqrt[6]t-1+1}{\sqrt[6]t-1}\,\mathrm dt=-\int\mathrm dt+\int\!\frac{1}{1^2-\left(\sqrt[12]t\right)^2}\,\mathrm dt=-x-5+\frac{1}{2}\ln\left|\frac{1+\sqrt[12]{x+5}}{1-\sqrt[12]{x+5}}\right|+C[/dispmath] Ali u rešenju je [inlmath]6\sqrt[6]{x+5}-6\log\left(1-\sqrt[6]{x+5}\right)+C[/inlmath]. Ne uočavam gde sam grešku mogao da napravim.