Question: Problem on the solution of a linear ODE with a free term of piecewise function

The solution Maple returns contains some piecewise indefinite integrals, but those indefinite integrals themselves are very simple to integrate, how can I make maple return solution with the indefinite integrals already being integrated?

The solution contains the following item,

Int(piecewise(t < T1, exp((1/2)*t*(1+2*I-I*sqrt(3))), t < T2, -1000*exp((1/2)*t*(1+2*I-I*sqrt(3)))*(-1/1000+T1-t), T2 <= t, -1000*exp((1/2)*t*(1+2*I-I*sqrt(3)))*(-1/1000-T2+T1)), t)



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