#2097 a integrate(sin(exp(x), x) is different to Mathematica

[Ching Guan Chao]

The results of integrate(sin(exp(x), x) is different from Mathematica 7
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Maxima version: 5.22.1
Maxima build date: 11:48 8/13/2010
Host type: i686-pc-mingw32
Lisp implementation type: GNU Common Lisp (GCL)
Lisp implementation version: GCL 2.6.8
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maxima:
b(t):= expand(float(subst(x=t, integrate(sin(exp(x)), x))));
makelist(b(t), t, 0, 3);
[-0.62471325642771,0.25024394235267,-0.073778082688431,-0.018588783055919]

Mathematica 7:
Table[SinIntegral[Exp[x]], {x, 0, 3}] // N
{0.946083, 1.82104, 1.49702, 1.55221}

[Dieter Kaiser]

The function SinIntegral in Mathematica corresponds in Maxima with expintegral_si.

(%i1) b(x):=float(expintegral_si(exp(x)));
(%o1) b(x) := float(expintegral_si(exp(x)))
(%i2) makelist(b(t),t,0,3);
(%o2) [0.946083070367183, 1.821040269147567, 1.497018244106465,
1.552207543269926]

This is the result of Mathematica too. The definition of the Exponential Integral Si is

integrate(sin(t)/t,t,0,x)

Maxima can not solve this integral symbolically.

Closing this bug report as "works for me".

Dieter Kaiser

[Aleksas Domarkas]

Proposition.
integrate(sin(exp(x)), x)+%pi/2 (Maxima)
=Integrate[Sin[Exp[x]], x] (Mathematica)
=integrate(sin(exp(x)), x) (Maple)

Maxima:
(%i1) integrate(sin(exp(x)), x)+%pi/2$
(%i2) makelist(subst(x=k,%),k,0,3)$
(%i3) float(%)$
(%i4) expand(%);
(%o4) [0.94608307036718,1.821040269147567,1.497018244106465,1.552207543738978]

Mathematica:
In[1]:= Integrate[Sin[Exp[x]], x]
Out[1]= SinIntegral[E^x]
In[2]:= Table[%, {x, 0, 3}]
Out[42]= {SinIntegral[1], SinIntegral[E], SinIntegral[E^2],
SinIntegral[E^3]}
In[3]:= N[%]
Out[3]= {0.946083, 1.82104, 1.49702, 1.55221}

Maple:
> integrate(sin(exp(x)), x);
Si(exp(x))
> seq(subs(x=k,%),k=0..3);
Si(exp(0)), Si(exp(1)), Si(exp(2)), Si(exp(3))
> evalf(%);
0.9460830704, 1.821040269, 1.497018244, 1.552207544