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?

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- Nov 15th 2009, 08:11 PMSunyataInverse Trigonometry.
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? - Nov 15th 2009, 08:20 PMredsoxfan325
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.