Discover the Integral of (k/x)-1/2 | Solve with Our Step-by-Step Guide

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Homework Statement



Integral of (k/x)-1/2

Homework Equations





The Attempt at a Solution


2(k/x)1/2

How do I find the integral of the inner function (k/x)?
 
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K is a constant, i presume. Put (1/x)^(-1/2) under the classical form x^a. Find a then apply the rules for integrating x^a you (probably) learned in class.
 

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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