Posted by **Terry** on Wednesday, September 3, 2008 at 7:10am.

What is the integral of 1/(x√(x^2-4)) dx?

So I know that I am going to have to factor out the 4 and use the arcsec trig identity but I've having trouble getting to a viable u-substitution.

I've gotten to factoring like this so far:

√(x^2-4) = √[2^2(x^2/2^2 - 1)] = 2√((x/2)^2 - 1))

I could do

u = x/2

du = 1/2 dx

But that still leaves the x in front of the radical.

How can I solve this?

- Math integral -
**David Q**, Wednesday, September 3, 2008 at 4:25pm
I'm extremely rusty at these, but I think it's possible you might be able to use the substitution x=2cosh(u), where cosh is the hyperbolic cosine. cosh²(u)-sinh²(u)=1, so sqrt(x²-4) = sqrt(4cosh²(u)-4) = 2sinh(u). dx/du=2sinh(u), so dx=2sinh(u)du, which cancels out with the square root in the denominator, leaving 2cosh(u) in the denominator to perform the integral on. I can't remember whether that's integrable or not: you'd need to look into that. Is that any help?

## Answer this Question

## Related Questions

- Calculus II/III - A. Find the integral of the following function. Integral of (x...
- Calculus - Am I allowed to multiply an entire integral (on the inside AND the ...
- trig integration - i'm having trouble evaluating the integral at pi/2 and 0. i ...
- calc - how do you start this problem: integral of xe^(-2x) There are two ways: 1...
- Calculus - I need help with this integral. w= the integral from 0 to 5 24e^-6t ...
- Calculus - I have two questions, because I'm preparing for a math test on monday...
- Math - Calculate the integrals if they converge. 10.) Integral from 1 to ...
- calculus - The problem is to evaluate the integral 10secxtanx dx, from -1/7 pi ...
- calc asap! - can you help me get started on this integral by parts? 4 S sqrt(t) ...
- Calc easy - Having trouble getting the correct solution. The integral of “x ...

More Related Questions