# What is #f(x) = int x/sqrt(x^2-1) dx# if #f(3) = 0 #?

##### 1 Answer

#### Explanation:

there's a very obvious pattern here

we know that

so we can trial estimate that if

then

so

and

you can of course play around with substitutions but seeing the pattern means that you can pretty much do the integration in your head. what i am really trying so say is that the integration is very trivial if you see the pattern, otherwise you need to get stuck into a lot of guessing and associated theory

it wold be interesting to see **that array of subs** that lead to an easy solution. i'd go for the simple

so, next, the initial value: