I am trying to integrate a logsumexp function which is a smooth function of another piecewise function.
Run
Integrate[ Log[Exp[s*a] + Exp[s*(a + v +a*t)]], {t, 0, (-v +vm)/a}, Assumptions -> {s > 0, a > 0, v >= 0, vm > 0}]
,
then, I got
(PolyLog[2, -e^(v * s)] - PolyLog[2, -e^(vm * s])] + a (-v + vm)*s^2)/(a*s)
.
But if I run
Integrate[ Log[Exp[s*a] + Exp[s*(a + v +a*t + (v +a*t)^2)]], {t, 0, (-v +vm)/a}, Assumptions -> {s > 0, a > 0, v >= 0, vm > 0}]
,
I cannot get any result.
s
,a
mv
,vm
, ...) by numeric values then you can apply numeric integration by usingNIntegrate
instead ofIntegrate
. $\endgroup$ – Henrik Schumacher Dec 11 '18 at 7:49Integration
, specificly the exampleIntegrate[x^x, x]
for which it is stated "This integral simply cannot be done in terms of standard mathematical functions. As a result, the Wolfram Language just leaves it undone. " $\endgroup$ – Bob Hanlon Dec 11 '18 at 17:24