# Integration Problems

Prologue
I am not sure exactly what is happening between the first part and second part. What happens to the 2?

Also, what technique do you use to integrate after that? I am a little unsure as to what slick moves are being used here. Any help is appreciated.

http://img511.imageshack.us/img511/2091/14157612rc6.jpg [Broken]
http://g.imageshack.us/g.php?h=511&i=14157612rc6.jpg [Broken]

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snipez90
I don't understand the context this is in but it looks like the 2r(dr) is being replaced by the substitution d(r^2) = 2r(dr) (this resembles usub, but I've never encountered this before). The denominator in the first step is just brought up top with a negative exponent. From step two to three, it looks like polynomial integration.

Hmm are you learning electromagnetism right now?

Prologue
Yep electromagnetism. It is out of the first chapter on the subject in Serway and Jewett. The example is for finding the electric field on a disk.

I am really stuck on that two, it seems like it has to be a mistake. There is probably some perspective I am missing here, that dr*2r=dr^2, but I am not seeing it now.

I can work it out fine with a substitution, but I really like to understand everything I encounter, and this doesn't mesh well.

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Big-T
If you let u = r^2, then you would replace 2rdr with du, wouldn't you?
Here, they have just not bothered renaming r^2.

Prologue
If you let u = r^2, then you would replace 2rdr with du, wouldn't you?
Here, they have just not bothered renaming r^2.

Perfect, yep that is the angle I was missing. Of course I made the substitution u=x^2 +r^2 so du=2rdr. So thinking this way, keep going du=d(x^2+r^2)=d(r^2) etc.