Integral of x / ((a-x)^2+b^2)^2 ?

mmm0036 · 2011-05-16T15:08:57+00:00

Integral of x / ((a-x)^2+b^2)^2 ? Homework Statement Find the integral of x / [(a-x)^2+b^2]^2 Homework Equations None really... integration by parts or Trigonometry substitution maybe: The Attempt at a Solution I tried but I didn't get solution.

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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Homework Statement

Homework Equations

The Attempt at a Solution

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

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