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

[rtoy]

Imported from SourceForge on 2024-07-09 17:55:41 Created by observerchao on 2010-10-31 03:39:42 Original: https://sourceforge.net/p/maxima/bugs/2097

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The results of integrate(sin(exp(x), x) is different from Mathematica 7 ------------------------------------------------------------- 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 -------------------------------------------------------------

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}

[rtoy]

Imported from SourceForge on 2024-07-09 17:55:42 Created by crategus on 2010-10-31 11:46:38 Original: https://sourceforge.net/p/maxima/bugs/2097/#a64b

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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

[rtoy]

Imported from SourceForge on 2024-07-09 17:55:46 Created by crategus on 2010-10-31 11:46:38 Original: https://sourceforge.net/p/maxima/bugs/2097/#6a35

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• status: open --> closed

[rtoy]

Imported from SourceForge on 2024-07-09 17:55:49 Created by alex108 on 2010-10-31 20:30:20 Original: https://sourceforge.net/p/maxima/bugs/2097/#6787

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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