Math integral

posted by .

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 -

    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?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus II/III

    A. Find the integral of the following function. Integral of (x√(x+1)) dx. B. Set up and evaluate the integral of (2√x) for the area of the surface generated by revolving the curve about the x-axis from 4 to 9. For part …
  2. Math/Calculus

    How would I solve the following integral with the substitution rule?
  3. Calculus

    so we are doing integrals and I have this question on my assignment and I can't seem to get it, because we have the trig substituion rules, but the number isn't even so its not a perfect square and I just cant get it, so any help would …
  4. Calculus

    Am I allowed to multiply an entire integral (on the inside AND the outside) by negative 1?
  5. Calculus

    I have two questions, because I'm preparing for a math test on monday. 1. Use the fundamental theorem of calculus to find the derivative: (d/dt) the integral over [0, cos t] of (3/5-(u^2))du I have a feeling I will be able to find …
  6. Calc

    Hello im trying to integrate tan^3 dx i have solved out the whole thing but it doesnt match up with the solution.. this is what i did: first i broke it up into: integral tan^2x (tanx) dx integral (sec^2x-1)(tanx) dx then i did a u …
  7. Calc

    Hello im trying to integrate tan^3 dx i have solved out the whole thing but it doesnt match up with the solution.. this is what i did: first i broke it up into: integral tan^2x (tanx) dx integral (sec^2x-1)(tanx) dx then i did a u …
  8. Calculus

    Evaluate the definite integral. dx/(x*sqrt(lnx)) from 1 to e^4 I'm having trouble figuring this out, I might be overthinking it. The way I've approached this is by using u substitution and letting u=lnx. I keep getting the wrong answer …
  9. Calculus

    Use the identity sin^2x+cos^2x=1 and the fact that sin^2x and cos^2x are mirror images in [0,pi/2], evaluate the integral from (0-pi/2) of sin^2xdx. I know how to calculate the integral using another trig identity, but I'm confused …
  10. Calculus Question! ASAP!

    Hello! I have this problem: x(dx)/sqrt(9-x^2) I was wondering why I can't use trig substitution and substitute sqrt(9-x^2) for sqrt(1-sec^2) and having: integral x = 3sin(theta) dx = 3cos(theta)d(theata) integral 3sin(theta)(3cos(theta))/3cos(theta) …

More Similar Questions