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Avoid error while calculating an integral with Wolfram Language? W|A is ok

Hi everyone This is the problem: When i calculate the integral

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

the output is:

img01,

So, what does it means?

In WholframAlpha the solution is: img2

And it can be solve "step-by-step". Why Mathematica does not work in the same way?

thank you very much for your help.
POSTED BY: Camilo Ramirez
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I think it would be helpful if symbolic functions like Integrate and Minimize automatically rationalized their inputs, rather than calling the numerical version (NIntegrate or NMinimize).
POSTED BY: Frank Kampas

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...
POSTED BY: Sander Huisman

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]

Please submit as Product Feedback on https://www.wolfram.com/support/contact/email/ Thanks!
POSTED BY: Sander Huisman
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