Question

Integrate:
This is to be solved by shortest way possible such that it can be solved in a maximum of 1 minute time or 2-3 steps..
The question is mentioned below:

Answer 1

\[\int\limits_{?}^{?} dx/\sqrt{(x-1)(x-2)}\]

Answer 2

there are no integrating limits..

Answer 3

you mean indefinite integration right??

Answer 4

\[
\int\frac{dx}{\sqrt{(x-1)(x-2)}}
\]

Answer 5

try method of completing squares
x^2 - 3x +2 = x^2 - 2 * 3/2 x + 9/4 - 9/4 +2

Answer 6

yeah @nbouscal that is my qsn

Answer 7

dont put _{}^{} ... just put \int in you latex for that

Answer 8

(x-2)(x-1) = (x - 3/2)^2 -1/4

substitute x-3/2 = u

it reduces to statndard form of
\[ \int \frac{1}{\sqrt{x^ 2 - 1 }} dx\]

if you know the formula ... shortcut .. you can solve it in next two steps

Answer 9

First you want to pull out that 1/4 though, so you'd have \[
\left(\frac{x-3/2}{\sqrt{1/4}}\right)^2-1
\]Right?

Answer 10

Oops ... sorry .. my mistake!!

Answer 11

None of the option contain ln or natural log..

Answer 12

so far i know, it leads to natural log or \[\cosh ^{-1}.............something.....\]

Answer 13

Wolf's solution does use a natural log, and uses basically the same method experimentX suggested.

Answer 14

\[a) 2xy (\sqrt{x-1}+\sqrt{x+1}) +c\]\[b) xy(\sqrt{x-1}+\sqrt{x-2})+c\]\[a)2xy(\sqrt{x-1}-\sqrt{x-2})+c\]\[d)\sin ^{-1}\sqrt{(x-1)/(x-2}+c\]
thesee are the options.

Answer 15

*these

Answer 16

try differentiating these ... you must get the function inside your integration!!

Answer 17

http://www.wolframalpha.com/input/?i=differentiate+sin^%28-1%29%28sqrt%28%28x-1%29%2F%28x-2%29%29%29%2Bc+with+respect+to+x

Answer 18

try verifying the rest ...

Answer 19

I guess none options match..