Integrate m/(am+bv) w/ Respect to v - Help!

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Homework Statement


i cannot figure out how to integrate m/(am+bv) with respect to v where a, b and m are constants. i don't know if there's some simple thing I've forgotten but i can't reduce it to a constant and a simple function of v. I'm getting really frustrated as I've been working on the bigger problem (this is only a small fraction of it) for over half an hour now. please help!
 
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nvm. I'm dumb.
 

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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