Integration Question

[uberathlete]

Hi all. My question is... how do I find the integral of: 1/(x*sqrt(x-4))

I've tried integrating by trigonometric substitution but it's not working. Any help on this would be greatly appreciated. Thanks!

 

[stapel]

There may be a better way of doing this, but....

1) Use the substitution "\(\displaystyle \sqrt{x\,-\,4}\,=\,u\)". This should (if I've done things correctly) give you:


. . . . .\(\displaystyle \large{\int{\,\frac{2}{u^2\,+\,4}\,}du}\)


2) Then use the formula you memorized for the derivative of the inverse tangent, along with some judicious rearranging and substituting, to integrate the result from (1).

3) Back-substitute to get an expression in terms of "x".

...but if somebody suggests something else, go with that instead! :shock:

Eliz.

 

[galactus]

Stapel's suggestion is as good as any. But are you sure that isn't an \(\displaystyle x^{2}\) in the radical?. Trig sub would work well then.

 

[uberathlete]

Got it! Thanks Stapel.

 

[stapel]

Got it!

Great!

Eliz.