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

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The integral 1/(x(sqrt(x^2 - 4)) requires a trigonometric substitution for an effective solution. The user initially attempted a u-substitution but encountered difficulties. It was noted that the user is currently studying Calculus BC and is still learning basic integration techniques. The discussion emphasizes the need for understanding trigonometric substitutions in solving this type of integral. Mastery of these concepts is essential for progressing in calculus.
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.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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