I'm trying to get the indefinite integral w.r.t. x of a very simple
function depending on a single parameter G, namely G/(x**2+G**2). I want to
assume the parameter G to be either one of three: general, positive, and
real. This is what I did
x=sp.symbols('x')
G=sp.symbols('G')
c = lambda x: G/(x**2+G**2)
u1=sp.integrate(c(x),x)
G=sp.symbols('G',positive=True)
c = lambda x: G/(x**2+G**2)
u2=sp.integrate(c(x),x)
G=sp.symbols('G',real=True)
c = lambda x: G/(x**2+G**2)
u3=sp.integrate(c(x),x)
print u1,'\n',u2,'\n',u3
This is what I get
-I*log(-I*G + x)/2 + I*log(I*G + x)/2
atan(x/G)
0
The 1st two I can understand, that 3rd one is completely unclear to me.
Should I expect this? Why?
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