∫ 3^xdx / sqrt(1+3^x)
Замена 1 + 3^x = t; dt = (ln 3)*3^x dx [m]\int \frac{3^{x}\ dx}{\sqrt{1+3^{x}}} = \frac{1}{\ln(3)} \cdot \int \frac{dt}{\sqrt{t}} = \frac{1}{\ln(3)} \cdot 2\sqrt{t} + C = \frac{2}{\ln(3)} \cdot \sqrt{1 + 3^x} + C[/m]