A curve with gradient function (1-x)/(1+x^2) goes through the origin. Show that the curve cuts the X-axis when arctan(x) = 0.5ln(1+x^2)
What exactly am I meant to do for these types of questions?
To find the original function you need to integrate
The first integral is (you should find this on any table of integrals) and the second integral can be solved using a simple u-sub ( ), so you end up with . Then you set to get the answer.
It seems a little strange that the question would ignore the presence of the integration constant though.