$$\int \frac{1}{x\sqrt{x^2+x+1}}\mathrm{d}x\; ;$$ $$\int\frac{6\sin(2x) + 6 + \ln(x^6)}{x\ln(x) + \sin^2(x)}\mathrm{d}x$$
I have done the first one using Euler's substitution, but I am not sure if it is correct, I have used the substitution for $a>0$, for the second one I have no idea how to start?