Integration (1 Viewer)

[Hotdog1]

What is the quickest way to integrate [x/x-1]^1/2? ta

 

[ezzy85]

multiply top and bottom by root x to make the top rational. then complete the square on the bottom.

 

[McLake]

Or subtract 1 add 1 to the top

[(x-1+1)/(x-1)]^1/2

cancel

[1 + 1/(x-1)]^1/2

let (cosx)^2 = 1/(x-1) giving

sinx

and intergrate

-cosx + C

and substitue back in

+/-[1/(x-1)]^1/2 + C

 

[Richard Lee]

Originally posted by Hotdog
What is the quickest way to integrate [x/x-1]^1/2? ta

let x=sec^2( u)

then the question changed to:

integrate : sec (u) / tan (u) d sec^2(u)

Try it, you will get it!

Good luck!

 

[Hotdog1]

Mclake: i idid it your way actually and it was a bit cumbersome, especially as it was a definite integral
ezzy: so what u do is integrate by parts with a substitution right?
Richard: sounds interesting, but then i got I {sec^3(u)du} and would the best way to proceed from there be by parts?

 

[ezzy85]

 

[Hotdog1]

I like it! THANKS!