Help with Integration Problem: Explicit Calculation Guide | PhysicsFans.org

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who can help me?how to derive (1)
please show me explict calculation
http://www.physicsfans.org/attachments/month_0706/20070608_115b22fb8b269180c1c7QsOB3UoXbLLO.gif
 
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Nobody's going to do your work for you. The guidlines of this forum state that you need to show some work before you get help.
 
This integral isn't tough, its just bloody long! For the inner integral:

\frac{a-b}{c}ln(\frac{b+c-cx_2}{b})-\frac{a}{c}x_2

Here, a=1-x_2

b=\lambda^2(1-x_2)c=q^2x_2-\lambda^2.

For the second integral, you're on your own mate... good luck.
 

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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