
semi complex integration
Hey, after taking a one year break of math (bad idea!) got this hw assignment that involves finding the integral of
(3)
l SQRT(4x^2 + 4 + (1/(x^2))) (the integral from one to three,
(1)T , the antiderivative would be perfect, and if you could walk me through the steps? Don't have my old calc book and havent been able to find it online. Thank you very much)

I assume this is what you mean:
$\displaystyle \int\sqrt{4x^{2}+4+\frac{1}{x^{2}}}dx$
If so, it can be rewritten without the radical as:
$\displaystyle \int\sqrt{\frac{(2x^{2}+1)^{2}}{x^{2}}}dx=\int\fra c{2x^{2}+1}{x}dx=2\int xdx+\int\frac{1}{x}dx$
Now, you have two very easy integrals. Just integrate and use your limits of integration.
