Question

\[\LARGE \int \frac{9-\sqrt x}{3-\sqrt x}dx\]
Can't even start... need some help.

Answer 1

http://www.wolframalpha.com/input/?i=simplify+%289-sqrt%28x%29%29%2F%283-sqrt%28x%29%29 this is worthless...

Answer 2

I think maybe writing u = sqrt(x) and du = (1/2)1/sqrt(x) might simplify a bit, but if you follow this way you will have to do long division again... Wonder if there is a smart trick to simplify.

Answer 3

\[ \frac{9 - \sqrt x}{3 - \sqrt x} = 1 + \frac{6}{3 -\sqrt x}\]

I think ...

Answer 4

^ That looks easier compared to what I got.

Answer 5

well @bmp I guess you have to answer this first lol http://openstudy.com/study#/updates/4fa03ee2e4b029e9dc314772 @experimentX ...how did that come, I want to know how to do it, I can't keep asking for every integral I have :(

Answer 6

It's just a way of polynomial division: http://en.wikipedia.org/wiki/Polynomial_long_division

Answer 7

so, without knowing how do to "long division" I'm not actually capable to solve these integrals , am I ? :(

Answer 8

Well, if you learned some other way of doing polynomial division, it should work fine. But if don't know that, I guess, yeah, you should look into learning it :-)

Answer 9

and if try this:
\[(6+3-\sqrt{x})/3-\sqrt{x}=6/(3-\sqrt{x}) +1\]

Answer 10

KhanAcademy has videos to cover that, tho. So, it shouldn't be too hard to pick up.

Answer 11

later make variable change x=t^2 and should be easy

Answer 12

ahh that's cool then, I'll just check khan academy. Thanks everyone for help\suggestions and everything... I'm wondering, to who should I give a medal now? :S ... (You give medals to each other, and I'll give one to the last) .. ;)

Answer 13

No problem. And polynomial division seems daunting at first because it's messy, but it's not that hard :-)

Answer 14

;) ... I'll see what I can do. ♥