So the following process involves W(t) which is Brownian Motion, and I need to prove that it is a martingale.(adsbygoogle = window.adsbygoogle || []).push({});

X_{t}=log(1+W(t)^{2})-∫_{0}^{t}(1-W(s)^{2})/(1+W(s)^{2})^{2}ds

The problem I am having is the integral. My professor did a lot of integrals w.r.t. W(t), but he didn't do very many integrals where W(t) was in the integrand and we were differentiating w.r.t. t.

I feel like I am going to use Ito's formula/rule, but I'm not sure how. I'm still a bit unclear on what is "allowed" with derivatives and integrals of Brownian motion, and w.r.t. Brownian motion. Any recommendations or suggestions as to a direction would be great.

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# How do you prove that this is a Martingale

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