Solve Indefinite Integral: 1/(x(sqrt(x^2 - 4)))

sausu
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Homework Statement



integral 1/(x(sqrt(x^2 - 4)))

Homework Equations



I don't know if there are any "equations" for integrals...


The Attempt at a Solution



Int(1/(x(Sqrt(4(x^2 /4)-1)
Int(1/(2x(Sqrt((x^2 /4)-1)
1/2 int(1/(x(Sqrt((x /2)^2)-1)
U-sub
u=x/2
du=1/2 dx
2du= dx
(This is where I hit a wall..I have no clue what I'm doing)
 
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For this one, you'll want to use a trig substitution instead of a regular u-substitution.
 
Bohrok said:
For this one, you'll want to use a trig substitution instead of a regular u-substitution.

We never learned how to do a trig substitution...
BTW I'm only in Calculus BC. We're just learning the basics of integrating.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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