I do not see a real problem, because we can verify the following:

(%i1) (s^2 * exp(- (a+b) * s^2 ));

(%o1) s^2*%e^((-b-a)*s^2)

(%i2) integrate(%,s);

(%o2) -gamma_incomplete(3/2,(b+a)*s^2)*s/(2*(b+a)^(3/2)*abs(s))

(%i3) diff(%,s);

(%o3) s^2*%e^-((b+a)*s^2)

We get back the integrand. I have compared the result with a result from Wolfram alpha. It is possible to expand the integral in terms of the erf function. The integrals differ by a constant term sqrt(%pi)/(4*(a+b)^3/2). That is the result of this bug report too. But this is not an error. The result might be not the expected result, but it is not wrong.

Setting the status to pending and the resolution to "works for me".

Dieter Kaiser