integrate(2^x/sqrt(1+4^x), x);
is not done.
but integrate(radcan (2^x/sqrt(1+4^x)), x);
works fine.
why this is odd? the risch algorithm should be decomposing stuff using
radcan.
It has to notice that 4^x is 2 ^(2*x) , and is therefore related to 2^x.
Macsyma has the same problem and the same fix.
This problem was posed as something the new "Fricas" can do.
RJF