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Example I have a problem with the highlighted step in the example, i couldn't quite understand how did he integrate that ?

trytryandtry
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1 Answers1

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Both sides of the equation are multiplied by $du/d\theta$ and then integrated with respect to $\theta$ (and multiplied by 2).

I suppose you could call this procedure “integrating with respect to $u$”, but I think that's a rather unclear way of explaining it.

Hans Lundmark
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  • Can you please go through the steps in more detail, I know it's just 2 steps but when i tried it i didn't quite get it – trytryandtry May 22 '20 at 16:31
  • It's perhaps easier to do it backwards? Take the derivative of the last equation with respect to $\theta$, using the chain rule (so that $(u^4)'=4u^3 u'$ and $((u')^2)'=2u'u''$, etc.). – Hans Lundmark May 22 '20 at 17:02