Integral Value Calculation: Physics Problem Solving

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Hi all while solving a problem of physics i came across integral (from 0 to infinity) of (sinkr/r3) dr.What is the value of this integral and how to calculate it. Please help me
Thanks
 
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The "value" of the integral is infinity, a.k.a. it does not converge.
Only for sin(kr)/r one can do the integration. Are you sure this is not what you meant? It looks like the typical integral coming from an integration over all space in spherical coordinates, which also introduces a Jacobian of r^2 sin(theta).
 

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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