Finding the Derivative of an Integral: Explanation Needed

[juice34]

1. Homework Statement
Can someone help me take the derivative of the integral
u(1/r)((d/dr)[(r)(dV/dr)])=P


2. Homework Equations



3. The Attempt at a Solution
my attempt yields V=(Pr^2)/(2u)+C(1), which is not right. The actual answer is V=(Pr^2)/4u+C(1)ln(r)+C(2). I am having trouble finding out where the 4 and everything else comes from could someone please explain to me what is going on. Thank YOU

 

[l'Hôpital]

When you first integrated, did you include your constant? If not, that might explain why you lacked the extra term upon the second integration.

 

[HallsofIvy]

You want to find
$$\frac{d}{dx}\int u(1/r)\frac{d\left(r\frac{dV}{dr}\right)}{dr}dr$$?
That, of course, is equal to
$$u(1/r)\frac{d\left(r\frac{dV}{dr}\right)}{dr}$$?

Or do you mean the integral of that integral?

 

[LCKurtz]

This is apparently a duplicate of the thread

https://www.physicsforums.com/showthread.php?p=2384640#post2384640