Question

So I am confused with the u^(1/2) and the -2u^(-1/2).

I said u/sqrt u is equal to u*sqrt U/U which = sqrt(u) so I get that is u^(1/2). But can't you rationalize the 2/sqrt(u) also? Would it not be 2*sqrt*u)/u? Since nothing cancels is it better not to rationalize it or what?

Answer 1

There's no real need to rationalize the denominator in the second term, since

$\dfrac2{\sqrt u}=\dfrac2{u^{1/2}}=2u^{-1/2}$

and this term is ready to be integrated via the power rule. Rationalizing doesn't really help here.