Mathematica does not simplify divergent integrals

Question

I get this as output:
$frac{1}{6} int_0^{infty } 6 t , dt$
Why it cannot cancel the coefficients?

Alexei Boulbitch · Answer

As much as I know, Mma does not simplify any integrals. However, one can help it. Try the following. Let us first introduce a rule:
intRule = 
  Inactivate[Integrate[exprA___ exprB__ , {var_, lim__}], Integrate] /;
     FreeQ[{exprB}, var] :> 
   exprB Inactivate[Integrate[exprA , {var, lim}], Integrate];

Here is your integral (inactivated):
expr1 = Inactivate[1/6*Integrate[6*t, {t, 0, [Infinity]}], Integrate]

(* 1/6 Inactive[Integrate][6 t, {t, 0, [Infinity]}]  *)

Now
expr1 /. intRule

(* Inactive[Integrate][t, {t, 0, [Infinity]}] *)

Have fun!

Mathematica does not simplify divergent integrals

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