How would you solve...

Question

anonymous · Answer

$$\int\limits_{?}^{?} \frac{ 1+x }{ 1+\sqrt{x} }dx$$

anonymous · Answer

Are the limits unknown or something?  Is this an indefinite integral?

anonymous · Answer

Perhaps try to rationalize the denominator by multiplying top and bottom by: $$
1-\sqrt{x}
$$That's one gues.

anonymous · Answer

yeah, it's an indefinite integral, don't mind the limits

anonymous · Answer

but if I do that, wouldn't it make things harder? 
$$\int\limits_{}^{}\frac{ (1+x)(1-\sqrt{x}) }{1-x  }dx$$

hartnn · Answer

one of the way is to perform long division after the substitution, $\sqrt x =u$.
but, if there are limits, do you mind to post what are they, maybe there is an easier way out.

anonymous · Answer

no, it's an indefinite integral, it's just that i forgot to erase the ? signs

hartnn · Answer

oh, then i would suggest you  ' to perform long division after the substitution, √x=u.'

anonymous · Answer

Hey, I tried that substitution and it works! Thanks a lot!

hartnn · Answer

welcome ^_^