1. ## [SOLVED] Integral

How would you solve $\int \ln (\sqrt{x^2+x+1}) dx$?
I don't see any good substitution nor a good integration by part. I'm not asking the whole solution, just the way you'd solve it.
Thanks.

2. Note that $\log((x^2+x+1)^{1/2}) = \frac{1}{2}\log\Big(\frac{x^3-1}{x-1}\Big)$

$=\frac{1}{2}\Big(\log(x^3-1)-\log(x-1)\Big)$

3. $\frac{1}{2}\int1.\ln(x^2+x+1)dx=\frac{x}{2}\ln(x^2 +x+1)+$...............