I want to integrate the following equation over the variable (l), which represents lambda, and evaluate it over 400 to 1100. I am unable integrate and seek assistance.The warning message I get is:Warning: Explicit integral could not be found.

clc;
clear;

T=5778;               %K, Black Body Temp
h=6.6260693*10^-34;   %Js, Plancks Constant
c=2.99792458*10^8;    %m/s, Speed of Light
K=1.3806505*10^-23;   %J/K, Boltzmann Constant

% Integration of Specteral Irradiance over the Wavelength (400-1100 nm)
%Elambda= Specteral Irradiamce
syms l
Elambda = ((2*pi*h*(c^2))/((l^5)*((exp((h*c)/(l*K*T)))-1)));
int(Elambda, l, 400e-9, 1100e-9)

[Walter Roberson]

I do not know why it is unable to integrate that.

With Maple I get an answer fairly quickly:

Q := v->convert(v, rational);
T := 5778;
h := Q(6.6260693*10^(-34));
c := Q(2.99792458*10^8);
K := Q(1.3806505*10^(-23));
Elambda := 2*Pi*h*c^2/(l^5*(exp(h*c/(l*K*T))-1));
simplify( int(Elambda, l = Q(400*10^(-9)) .. Q(1100*10^(-9))), size)

The result is

(2540160233662625000000000000000000/3570512327073093175738239)*Pi*(I*Pi-(9730585744557790520259757668384832387240388623974704382705040286060555230742900630360966869322583867068019/372436702541254268800273766911139944549529040826951558815596730324962499047308073940184365356445312500000000)*polylog(4, exp(335090366532852037571247381167500000/148026422442236354716865598331930097))-(64/1267)*ln(-1+exp(335090366532852037571247381167500000/148026422442236354716865598331930097))+(53733591346531796762222212194490625211/106139873599280882900692607984805625000)*polylog(2, exp(83772591633213009392811845291875000/13456947494748759519715054393811827))-(723090117454564686079897663311300847364613444458930897322658842716170497/4445806143516702037865961585369280107990346951694254739096633398437500000)*polylog(3, exp(83772591633213009392811845291875000/13456947494748759519715054393811827))+(9730585744557790520259757668384832387240388623974704382705040286060555230742900630360966869322583867068019/372436702541254268800273766911139944549529040826951558815596730324962499047308073940184365356445312500000000)*polylog(4, exp(83772591633213009392811845291875000/13456947494748759519715054393811827))+(1331/1267)*ln(-1+exp(83772591633213009392811845291875000/13456947494748759519715054393811827))-(888158534653418128301193589991580582/13267484199910110362586575998100703125)*polylog(2, exp(335090366532852037571247381167500000/148026422442236354716865598331930097))+(65735465223142244189081605755572804305873949496266445211150803883288227/1111451535879175509466490396342320026997586737923563684774158349609375000)*polylog(3, exp(335090366532852037571247381167500000/148026422442236354716865598331930097))-43038168951563183575557085518700781250/26792782462044780203752673298079347557)

which is about 4.068391609*10^7-2.235015034*I

I don't think you were expecting a complex result, so I suggest you recheck your formula for Elambda

[Osvaldo Rodriguez]

Robert,

Thank you for your input. I am not familiar with Maple, and not in anyway an expert on Matlab, so I will do some digesting on this one because I also did expect a complex result. Thanks