integrate dx/ sqrt (x^2 - x + 1) throughb reciprocal substitution
i tried solving but i was stuck in
du / u x sqrt (1-u+u ^2)
u = 1/x
Dear sean,
$\displaystyle \int{\frac{dx}{\sqrt{x^{2}-x+1}}}$
$\displaystyle \int{\frac{dx}{\sqrt{\left(x-\frac{1}{2}\right)^{2}-\frac{1}{4}+1}}}$
$\displaystyle \int{\frac{dx}{\sqrt{\left(x-\frac{1}{2}\right)^{2}+\frac{3}{4}}}}$
Now substitute $\displaystyle x-\frac{1}{2}=\frac{\sqrt3}{2}tanU$
See if you can do it from here. If you need more assistance please don't hesitate to reply me.