不知你的2-t整个是分子,还是只有t是分子,我按只有t是分子做了
∫1500(2-t/(2t+5)) dt
=750∫(4-2t/(2t+5)) dt
=750∫(4-(2t+5-5)/(2t+5)) dt
=750∫(3 + 5/(2t+5)) dt
=750∫(3 + 5/(2t+5)) dt
=750(3t + (5/2)ln|2t+5| + C)