integrate this one please.

Question

kaiz122 · Answer

$$\int\limits_{}^{} \frac{\sqrt{x+9}}{x} dx$$

kaiz122 · Answer

@amistre64

anonymous · Answer

difficult, indeed :D

foolaroundmath · Answer

Try $x+9 = t^{2}$ Then, you'll probably need to use partial fractions.

amistre64 · Answer

can we rewrite it?$$\sqrt{\frac{x+9}{x^2}}$$

is a thought i have, then split that or work about it

kaiz122 · Answer

@FoolAroundMath  i have already tried that, and i got a wrong answer, i don;t know where i got wrong, @amistre64 i'll try it.

amistre64 · Answer

a complicated by parts might be suitable as well http://www.wolframalpha.com/input/?i=integrate+sqrt%28x%2B9%29%2Fx but i gotsta feed the kids, good luck

foolaroundmath · Answer

$x+9 = t^{2} \implies dx = 2t \text{ d}t$ $$\int \frac{2t^{2}}{t^{2}-9}dt = \int \frac{2(t^{2}-9)+18}{t^{2}-9}dt = \int (2 + \frac{18}{t^{2}-9})dt$$

kaiz122 · Answer

@amistre64 my answer was $$2\sqrt{x+9} -3 \ln (\sqrt{x+9} +3)+3 \ln(\sqrt{x+9}-3) +C$$

kaiz122 · Answer

so is it a correct answer?  thought it was wrong.

foolaroundmath · Answer

It's correct but you need a $|.|$ sign in the $\ln{(|\sqrt{x+9}-3|)} $. because integral of $\int dt/t = ln(|t|)$

kaiz122 · Answer

yes, it should have had. i just forgot it while typing here.