Hi guys!

I've got a problem with some indefinite integrals...

I don't want to solve them using neither the substitution method, nor the parts one, and that's why I'm experiencing some problems...

So for example, the integral of x/(1+4x^2) = 1/8 ln (4x^2+1), I get it, because (4x^2)=8x... however, I don't get why the integral of 1/(4x^2+1) is 1/2 arctan (2x), why is it 1/2 and why is it 2x?

The same doubt arises when it is let's say 1/(1+3x^2)...

I tried using the wolframalpha calculator, but it doesn't show the steps taken in order to achieve the right function...

I guess it has something to do with 1 being the numerator, instead of x, but even so I don't understand why...

Thank you guys!