vpa can not be used? why "numeric::int...." appearing?

Hi any body could help me to resolve this issue? I have a function to integrate w.r.t E by keeping V and z as constants from 0 to inf. When I use inbuilt 'int', I got the results as "Explicit integral could not be found". Some suggested to go for vpa(X,5), yet I couldn't resolve it. Any helps would be appreciated. Thanks.

syms E V z

f= -(160822346162939158374951306007842683360580644730317667175195738112000000000000000*E*((315656633149031*sin((75557863725914323419136*pi*z*((10000*E)/3543 + 1)^(1/2)*((5534527050034529*E)/140737488355328)^(1/2))/315656633149031))/(75557863725914323419136*pi*z*((10000*E)/3543 + 1)^(1/2)*((5534527050034529*E)/140737488355328)^(1/2)) - 1))/(618501041962717063047950574462370983128147*(exp((5534527050034529*E)/140737488355328 + (5534527050034529*V)/140737488355328 - 7742803342998306071/14073748835532800) + 1)*((98722420244898788167299958078358473932800*((6877444662696557*E)/618970019642690137449562112)^(1/2))/(100093691394021*((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 + (((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 - 15026719/25000000000)^2 - ((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000)^3)^(1/2) - 15026719/25000000000)^(1/3)) - (((98722420244898788167299958078358473932800*((6877444662696557*E)/618970019642690137449562112)^(1/2)*((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000)^2)/33364563798007 - (604921630050617324495130493125141549023232*((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 - 15026719/25000000000)*((6877444662696557*E)/618970019642690137449562112)^(1/2))/834114094950175)/(2*(((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 - 15026719/25000000000)^2 - ((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000)^3)^(1/2)) - (302460815025308662247565246562570774511616*((6877444662696557*E)/618970019642690137449562112)^(1/2))/834114094950175)/(3*((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 + (((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 - 15026719/25000000000)^2 - ((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000)^3)^(1/2) - 15026719/25000000000)^(2/3)) + (3952027511271527982106121913080217600000*((6877444662696557*E)/618970019642690137449562112)^(1/2))/33364563798007 + ((((98722420244898788167299958078358473932800*((6877444662696557*E)/618970019642690137449562112)^(1/2)*((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000)^2)/33364563798007 - (604921630050617324495130493125141549023232*((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 - 15026719/25000000000)*((6877444662696557*E)/618970019642690137449562112)^(1/2))/834114094950175)/(2*(((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 - 15026719/25000000000)^2 - ((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000)^3)^(1/2)) - (302460815025308662247565246562570774511616*((6877444662696557*E)/618970019642690137449562112)^(1/2))/834114094950175)*((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000))/(3*((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 + (((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 - 15026719/25000000000)^2 - ((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000)^3)^(1/2) - 15026719/25000000000)^(4/3))))

X=int(f,E,0,inf) Warning: Explicit integral could not be found.

X =

int(-(160822346162939158374951306007842683360580644730317667175195738112000000000000000*E*((315656633149031*sin((75557863725914323419136*pi*z*((10000*E)/3543 + 1)^(1/2)*((5534527050034529*E)/140737488355328)^(1/2))/315656633149031))/(75557863725914323419136*pi*z*((10000*E)/3543 + 1)^(1/2)*((5534527050034529*E)/140737488355328)^(1/2)) - 1))/(618501041962717063047950574462370983128147*(exp((5534527050034529*E)/140737488355328 + (5534527050034529*V)/140737488355328 - 7742803342998306071/14073748835532800) + 1)*((98722420244898788167299958078358473932800*((6877444662696557*E)/618970019642690137449562112)^(1/2))/(100093691394021*((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 + (((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 - 15026719/25000000000)^2 - ((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000)^3)^(1/2) - 15026719/25000000000)^(1/3)) - (((98722420244898788167299958078358473932800*((6877444662696557*E)/618970019642690137449562112)^(1/2)*((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000)^2)/33364563798007 - (604921630050617324495130493125141549023232*((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 - 15026719/25000000000)*((6877444662696557*E)/618970019642690137449562112)^(1/2))/834114094950175)/(2*(((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 - 15026719/25000000000)^2 - ((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000)^3)^(1/2)) - (302460815025308662247565246562570774511616*((6877444662696557*E)/618970019642690137449562112)^(1/2))/834114094950175)/(3*((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 + (((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 - 15026719/25000000000)^2 - ((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000)^3)^(1/2) - 15026719/25000000000)^(2/3)) + (3952027511271527982106121913080217600000*((6877444662696557*E)/618970019642690137449562112)^(1/2))/33364563798007 + ((((98722420244898788167299958078358473932800*((6877444662696557*E)/618970019642690137449562112)^(1/2)*((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000)^2)/33364563798007 - (604921630050617324495130493125141549023232*((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 - 15026719/25000000000)*((6877444662696557*E)/618970019642690137449562112)^(1/2))/834114094950175)/(2*(((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 - 15026719/25000000000)^2 - ((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000)^3)^(1/2)) - (302460815025308662247565246562570774511616*((6877444662696557*E)/618970019642690137449562112)^(1/2))/834114094950175)*((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000))/(3*((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 + (((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 - 15026719/25000000000)^2 - ((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000)^3)^(1/2) - 15026719/25000000000)^(4/3)))), E = 0..Inf)

vpa(X,5)

ans =

numeric::int(-(160822346162939158374951306007842683360580644730317667175195738112000000000000000*E*((315656633149031*sin((75557863725914323419136*pi*z*((10000*E)/3543 + 1)^(1/2)*((5534527050034529*E)/140737488355328)^(1/2))/315656633149031))/(75557863725914323419136*pi*z*((10000*E)/3543 + 1)^(1/2)*((5534527050034529*E)/140737488355328)^(1/2)) - 1))/(618501041962717063047950574462370983128147*(exp((5534527050034529*E)/140737488355328 + (5534527050034529*V)/140737488355328 - 7742803342998306071/14073748835532800) + 1)*((98722420244898788167299958078358473932800*((6877444662696557*E)/618970019642690137449562112)^(1/2))/(100093691394021*((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 + (((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 - 15026719/25000000000)^2 - ((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000)^3)^(1/2) - 15026719/25000000000)^(1/3)) - (((98722420244898788167299958078358473932800*((6877444662696557*E)/618970019642690137449562112)^(1/2)*((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000)^2)/33364563798007 - (604921630050617324495130493125141549023232*((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 - 15026719/25000000000)*((6877444662696557*E)/618970019642690137449562112)^(1/2))/834114094950175)/(2*(((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 - 15026719/25000000000)^2 - ((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000)^3)^(1/2)) - (302460815025308662247565246562570774511616*((6877444662696557*E)/618970019642690137449562112)^(1/2))/834114094950175)/(3*((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 + (((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 - 15026719/25000000000)^2 - ((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000)^3)^(1/2) - 15026719/25000000000)^(2/3)) + (3952027511271527982106121913080217600000*((6877444662696557*E)/618970019642690137449562112)^(1/2))/33364563798007 + ((((98722420244898788167299958078358473932800*((6877444662696557*E)/618970019642690137449562112)^(1/2)*((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000)^2)/33364563798007 - (604921630050617324495130493125141549023232*((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 - 15026719/25000000000)*((6877444662696557*E)/618970019642690137449562112)^(1/2))/834114094950175)/(2*(((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 - 15026719/25000000000)^2 - ((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000)^3)^(1/2)) - (302460815025308662247565246562570774511616*((6877444662696557*E)/618970019642690137449562112)^(1/2))/834114094950175)*((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000))/(3*((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 + (((34081300774431287738506648835156271556395069066039782704939008000000*E)/1113194117431279288697172049 - 15026719/25000000000)^2 - ((278101189509843229200380651449663578591555031138635517788160000000000*E)/3339582352293837866091516147 + 13522409/300000000)^3)^(1/2) - 15026719/25000000000)^(4/3)))), E = 0..Inf)

Answer 1

[Walter Roberson]

Your expression involves E and z. You can only use that form of numeric integration on a single variable.

vpa tries to create numeric solutions so it invokes the numeric form of the symbolic integration.

[MAH AB]

so is there any other alternative ways where I can integrate my function w.r.t E by keeping V and z as constant from 0 to inf? After integration I need a function that contains V and z. Thanks for any inputs.

[Walter Roberson]

No, your function is very steep and has significant values down to about E = 1e-43. With the normal 16 or so digits of computation the results even over very narrow areas are numeric noise. The fall off past about 14 is rapid. Your function is too steep for techniques such as Taylor series to be useful unless you used many terms.