Integration with square roots HELP

Quarkn
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Homework Statement



(8x+1)^0.5

Homework Equations





The Attempt at a Solution



I tried using substitution but it clearly doesn't work because nothing in the brackets equals when derived.

Anyone help me with the beginning steps?
 
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Substitute u=8x+1. I don't understand what your problem with that would be.
 
Dick said:
Substitute u=8x+1. I don't understand what your problem with that would be.

Yes, you are correct. I guess i had some other weird method in my head :S Substitution works, sorry!

Thanks!
 

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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