Integration Help: Solving S dx/(1-x^2)^(3/2) with Integration by Parts

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Homework Statement


S dx/(1-x^2)^(3/2)

Homework Equations


The Attempt at a Solution



I tried seperating the bottom

S 1/((1-x^2)^(1/2))(1-x^2)

then tried to use integration by parts... but I think that doesn't work..

how would I get the power to 1/2?

thank you in advance
 
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Thought about trying a trig. substitution? :smile:
 
Hi kira137! :smile:

(have a square-root: √ and try using the X2 tag just above the Reply box :wink:)

Alternative hint: can you integrate x2/(1 - x2)3/2 by parts ? :wink:
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

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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