What's the integral of u''(x)/u'(x)?

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What's the integral of u''(x)/u'(x)?
 
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you need to do u substitution
 
kasse said:
What's the integral of u''(x)/u'(x)?

If you were to call v = u'(x), what would u''(x) be? You can make a new integral in terms of v. If the result tells you what v is, you can now substitute back to find an expression in terms of u.
 
Of course, thank you!
 
Btw, how is u'' to be pronounced?

u prime prime? u double prime?
 
kasse said:
Btw, how is u'' to be pronounced?

u prime prime? u double prime?

"u double prime" is typical.
 

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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