Some integrals with problematic evaluation

[parisse]

Ok, we are doing the same change of variable, but then you are doing an additional rewriting command because atan(x/sqrt(a/b)) with x a tangent is not the same as atan(3sin(x)cos(x)/(2+sqrt(10)+3cos(x)^2)), this is the missing step.
I think I prefer an atan(tan(x)/sqrt(a/b)), because you can easily throw the floor part if you don't need a continuous antiderivative and then the answer is more compact. It seems the nspire does the same.
BTW, I don't need tex code, I prefer algebraic expressions that I can easily copy/paste.