a curious integral

Hello,

Can anyone suggest how to evaluate the following integral:

> Int(1/v/sqrt(v^2*a+b*v+c), v);

/
| 1
| ---------------------- dv
| 2
/ v sqrt(v a + b v + c)


Maple finds a surprisingly clean/simple answer:

> value(%) assuming c>0;

2 c + b v
arctanh(1/2 ------------------------)
1/2 2 1/2
c (v a + b v + c)
- -------------------------------------
1/2
c

I'm trying to understand where the "2c+bv" comes from....

thanks,
bugalore.

.

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