How to integrate $\left(1+\ln(x)\right)\sqrt{1+(x\ln(x))^2}$ with Risch algorithm?

Question

How would you integrate $\left(1 + \ln\left(x\right)\right)\, \sqrt{1 + \left(x\ln\left(x\right)\right)^{2}\,}$ using the Risch algorithm?

I want to know this because Mathematica is using the Risch Algorithm when integrating and can't do this integral even if it can be done by simple substitution. Is it even possible to integrate this using the Risch algorithm?