Question: strange result for integrating factor of an ODE

I might be doing something wrong here. But when I ask Maple 17 for the integrating factor of this ODE, it does not match the result if I find the integrating factor directly.

ode:=2*t*y(t)+t^2*(diff(y(t), t))+t^2*y(t)-2*y(t)-t*(diff(y(t), t)) = 0;
simplify(exp(int( (t^2+2*t-2)/(t^2-t),t)));

Why I am not getting the same result from the last 2 commands above?


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