Integrating 6/x^2: Step-by-Step Guide

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Homework Statement


I know the integral of 6/(x^2) is 6/x but what are the steps to achieve this...


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The Attempt at a Solution



Does it involve the substitution u=(x^2) then what is the next step...

thanks
 
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What is the derivative of your substitution? Does it appear in your original Integral?

Try re-writing your Integral as \int6x^{-2}dx do you see what to do next?
 
Oh ofcourse - you would then say add one to the power and divide by the new power which becomes -6/x

thanks - (i must have had a mental block :) )
 
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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