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.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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