NIntegrate can only handle integrals that would result in a number. So NIntegrate[0.4 a b, {b, 0, 1}] can't be done (but Integrate[0.4 a b, {b, 0, 1}] can be done). So I'm not sure if Integrate always calls NIntegrate when there are approximate values...

Hi Camilo,

I agree with you that the error should not happen, but it is caused by giving approximate values. Compare:

Integrate[500 (1.4 - Log[0.5 t + 1])/(t + 2), t]

and

Integrate[500 (7/5 - Log[t/2 + 1])/(t + 2), t]

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