Question

DEFINATE INTEGRAL: please assist - integral of
1/(x -sqrtx) from 4 to 9

Answer 1

\[\int\limits_{4}^{9}\frac{ 1dx }{ x-\sqrt{x} }\]

Answer 2

put\[\sqrt{x}=t,x=t^2,dx=2t~dt\]
when x=4
\[t=\sqrt{4}=2\]
when x=9,
\[t=\sqrt{9}=3\]
\[I=\int\limits_{t=2}^{3}\frac{ 2t~dt }{ t^2-t }=2\int\limits_{2}^{3}\frac{ dt }{t-1 }=?\]

Answer 3

I've experimented with this problem and have seen that a simple substitution will greatly simplify this integration. Have you @mertich, considered a substitution yet?

Answer 4

thanx thanx ! thanx

Answer 5

I TRIED LET u =x, and i got du =1dx but as i further intergrated, i found that: ln(u -sqrt u) and inserting the limits i got ln6-ln2 = ln3, well its wrong because its ln4! I don't understand---

Answer 6

@mathmale