I have a problem i dont have the solution manual too and i am stumped on how to complete.

This could be a trigonometric substitution?

$\displaystyle \int_1^2 \frac {dx}{x \sqrt {4 + x^2}}$

this is what i came up with but i dont think its right..

$\displaystyle x = 2 tan \theta$

$\displaystyle dx = 2 sec^2 \theta$

and

$\displaystyle \sqrt {2^2 + ( 2tan \theta)2}}$

identity

$\displaystyle (tan^2\theta -1)2^2$

=$\displaystyle 2sec\theta$

substitute back in to the original equation..

$\displaystyle \int_1^2 \frac{2 sec^2 \theta} {2 tan\theta 2 sec\theta}2 sec^2\theta$

cross multiply

$\displaystyle \int_1^2 \frac{2 sec^2 \theta} {2 tan\theta}$

not sure if the 2 can cross out or what to do with them or if i am even right at this point?