can't integrate 1 / (1 + Sqrt(x))

[medovina]

Yacas can't integrate 1 / (1 + Sqrt(x)):

In> Integrate(x) 1 / (1 + Sqrt(x))
Out> Integrate(x)1/(Sqrt(x)+1)

The integration is not difficult via a substitution u = 1 + Sqrt(x). The answer should be

2*(Sqrt(x)+1)-2*Ln(Sqrt(x)+1)

[grzegorzmazur]

Unfortunately, it's not that easy to implement, as it'd require a more general strategy. Admittedly, integration is one of yacas weak spots. I'm considering reimplementing http://www-sop.inria.fr/cafe/Manuel.Bronstein/pmint/ in yacas, but before I actually do that I'd like to understand the issue a bit better.