a question about an integral
 

I was wondering what happens when the method of partial fractions is used for indefinite integrals I've always done for a real variable.

The integrand was

[TEX]\frac{1}{1+x^2}[/TEX]

the solution I got was

[TEX]\frac{i}{2}\frac{ln(1 + ix)}{ln(1 - ix)} + c [/TEX]

If there was nothing wrong with the method I used then the latter expression
is arctan(x) + c.

Was there anything wrong with my method?

Should have written

[TEX]\frac{i}{2}ln{\frac{(1 + ix)}{(1 - ix)} + c [/TEX]

Suggest you use the formula

[tex]e^{i\theta}\;=\;\cos{(\theta)}\;+\;i\sin{(\theta)}[/tex]