[SOLVED] Integral

arbolis · #1 $Old$ June 30th, 2009, 06:51 PM

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.

Bruno J. · #2 $Old$ June 30th, 2009, 07:10 PM

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

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

pankaj · #3 $Old$ June 30th, 2009, 07:44 PM

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