Simple converions to rational functions
Task number: 3112
Evaluate the following integrals (or at least convert to an integral of a rational function)
Variant 1
\( \int \frac{e^x}{e^x + 1} \, dx \)
Variant 2
\( \int\frac{1}{e^{2x} - 3 e^x - 4} \, dx \)
Variant 3
\( \int\frac{1}{1 + e^{x/6} + e^{x/3} + e^{x/2}} \, dx \)
Variant 4
\( \int\frac{1}{x(\ln^2 x - 5 \ln x + 6)} \, dx \)
