MATLAB: Vpa can not be used? why “numeric::int….” appearing

integrationnumerical integrationsymbolic integration

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)

Best Answer

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.

Related Solutions

MATLAB: Explicit integral could not be found

Explicit integral solution

MATLAB: I need final equation…

There are two solutions:

{

x = (1460*(-9685390482496000000*(-(1/2131600)*f^2 + (1/1065800)*g*f - (1/2131600)*g^2 + ((1/1460)*c - (1/1460)*d + a)*(-(1/1460)*c + (1/1460)*d + a))*((1/1460)*c - (1/1460)*e + b)*b^2*(-g + f)^2*(-(1/1460)*c + (1/1460)*e + b)*(b^2 - 2*a*b - (1/2131600)*f^2 + (1/1065800)*g*f - (1/2131600)*g^2 + (-(1/1460)*d + (1/1460)*e + a)*((1/1460)*d - (1/1460)*e + a)))^(1/2) + (4543718560000*a*d - 4543718560000*a*c)*b^3 + (2131600*c^3 - 2131600*d*c^2 + (9087437120000*a^2 - 2131600*d^2)*c + (-4263200*g*f - 4543718560000*a^2 + 2131600*g^2 + 2131600*f^2)*e - 4263200*f*g*d + 2131600*d*g^2 - 4543718560000*d*a^2 + 2131600*d^3 + 2131600*d*f^2)*b^2 + (-4263200*a*c^3 + (2131600*a*e + 2131600*a*d)*c^2 + (2131600*a*e^2 - 4543718560000*a^3 + (2131600*d^2 + 2131600*f^2 - 4263200*g*f + 2131600*g^2)*a)*c - 2131600*d*a*e^2 + (4543718560000*a^3 + (-2131600*d^2 - 2131600*g^2 - 2131600*f^2 + 4263200*g*f)*a)*e)*b + (-f^2 + 2131600*a^2 - g^2 + 2*g*f)*c^3 + (f^2 - 2131600*a^2 + g^2 - 2*g*f)*e*c^2 + (f^2 - 2131600*a^2 + g^2 - 2*g*f)*e^2*c + (-f^2 + 2131600*a^2 - g^2 + 2*g*f)*e^3) / ((4263200*d^2 + 4263200*c^2 + 4263200*g^2 + 4263200*f^2 - 8526400*d*c - 8526400*g*f)*b^2 - 8526400*a*(-e + c)*(c - d)*b + 4263200*(-e + c)^2*((1/1460)*f - (1/1460)*g + a)*(-(1/1460)*f + (1/1460)*g + a))
z = (1/4263200)*(((1460*d - 1460*c)*b + 1460*a*(-e + c))*(-9685390482496000000*(-(1/2131600)*f^2 + (1/1065800)*g*f - (1/2131600)*g^2 + ((1/1460)*c - (1/1460)*d + a)*(-(1/1460)*c + (1/1460)*d + a))*((1/1460)*c - (1/1460)*e + b)*b^2*(-g + f)^2*(-(1/1460)*c + (1/1460)*e + b)*(b^2 - 2*a*b - (1/2131600)*f^2 + (1/1065800)*g*f - (1/2131600)*g^2 + (-(1/1460)*d + (1/1460)*e + a)*((1/1460)*d - (1/1460)*e + a)))^(1/2) + 4543718560000*b*(-g + f)*(-a*(-g + f)*b^3 + ((1/1065800)*f*c^2 + ((-(3/2131600)*d - (1/2131600)*e)*f - (1/2131600)*g*(d - e))*c + (1/2131600)*f^3 - (1/2131600)*f^2*g + (a^2 + (1/2131600)*d*e - (1/2131600)*g^2 + (1/2131600)*d^2)*f - (-(1/2131600)*g^2 + (1/2131600)*d*e - (1/2131600)*d^2 + a^2)*g)*b^2 - (3/2131600)*(((1/3)*g + f)*c + (-(4/3)*d + (1/3)*e)*f - (1/3)*g*e)*a*(-e + c)*b + (1/2131600)*(-(1/2131600)*(-g + f)*(d - e)*c - (1/2131600)*f^3 + (1/2131600)*f^2*g + (a^2 + (1/2131600)*d^2 - (1/2131600)*d*e + (1/2131600)*g^2)*f + (-(1/2131600)*g^2 + (1/2131600)*d*e - (1/2131600)*d^2 + a^2)*g)*(-e + c)^2)) / (b*(-g + f)*((f^2 + d^2 - 2*g*f - 2*d*c + c^2 + g^2)*b^2 - 2*a*(-e + c)*(c - d)*b + (-e + c)^2*((1/1460)*f - (1/1460)*g + a)*(-(1/1460)*f + (1/1460)*g + a)))

}

and

{

x = (-1460*(-9685390482496000000*(-(1/2131600)*f^2 + (1/1065800)*g*f - (1/2131600)*g^2 + ((1/1460)*c - (1/1460)*d + a)*(-(1/1460)*c + (1/1460)*d + a))*((1/1460)*c - (1/1460)*e + b)*b^2*(-g + f)^2*(-(1/1460)*c + (1/1460)*e + b)*(b^2 - 2*a*b - (1/2131600)*f^2 + (1/1065800)*g*f - (1/2131600)*g^2 + (-(1/1460)*d + (1/1460)*e + a)*((1/1460)*d - (1/1460)*e + a)))^(1/2) + (4543718560000*a*d - 4543718560000*a*c)*b^3 + (2131600*c^3 - 2131600*d*c^2 + (9087437120000*a^2 - 2131600*d^2)*c + (-4263200*g*f - 4543718560000*a^2 + 2131600*g^2 + 2131600*f^2)*e - 4263200*f*g*d + 2131600*d*g^2 - 4543718560000*d*a^2 + 2131600*d^3 + 2131600*d*f^2)*b^2 + (-4263200*a*c^3 + (2131600*a*e + 2131600*a*d)*c^2 + (2131600*a*e^2 - 4543718560000*a^3 + (2131600*d^2+2131600*f^2 - 4263200*g*f+2131600*g^2)*a)*c - 2131600*d*a*e^2 + (4543718560000*a^3 + (-2131600*d^2 - 2131600*g^2 - 2131600*f^2 + 4263200*g*f)*a)*e)*b + (-f^2 + 2131600*a^2 - g^2 + 2*g*f)*c^3 + (f^2 - 2131600*a^2 + g^2 - 2*g*f)*e*c^2 + (f^2 - 2131600*a^2 + g^2 - 2*g*f)*e^2*c + (-f^2 + 2131600*a^2 - g^2 + 2*g*f)*e^3) / ((4263200*d^2 + 4263200*c^2 + 4263200*g^2 + 4263200*f^2 - 8526400*d*c - 8526400*g*f)*b^2 - 8526400*a*(-e + c)*(c-d)*b + 4263200*(-e + c)^2*((1/1460)*f - (1/1460)*g + a)*(-(1/1460)*f + (1/1460)*g + a))
z = (1/4263200)*(((-1460*d + 1460*c)*b - 1460*a*(-e + c))*(-9685390482496000000*(-(1/2131600)*f^2 + (1/1065800)*g*f - (1/2131600)*g^2 + ((1/1460)*c - (1/1460)*d+a)*(-(1/1460)*c + (1/1460)*d + a))*((1/1460)*c - (1/1460)*e + b)*b^2*(-g + f)^2*(-(1/1460)*c + (1/1460)*e + b)*(b^2 - 2*a*b - (1/2131600)*f^2 + (1/1065800)*g*f - (1/2131600)*g^2 + (-(1/1460)*d + (1/1460)*e + a)*((1/1460)*d - (1/1460)*e + a)))^(1/2) + 4543718560000*b*(-g + f)*(-a*(-g + f)*b^3 + ((1/1065800)*f*c^2 + ((-(3/2131600)*d - (1/2131600)*e)*f - (1/2131600)*g*(d - e))*c + (1/2131600)*f^3 - (1/2131600)*f^2*g + (a^2 + (1/2131600)*d*e - (1/2131600)*g^2 + (1/2131600)*d^2)*f - (-(1/2131600)*g^2 + (1/2131600)*d*e - (1/2131600)*d^2 + a^2)*g)*b^2 - (3/2131600)*(((1/3)*g + f)*c + (-(4/3)*d + (1/3)*e)*f - (1/3)*g*e)*a*(-e + c)*b + (1/2131600)*(-(1/2131600)*(-g + f)*(d - e)*c - (1/2131600)*f^3 + (1/2131600)*f^2*g + (a^2 + (1/2131600)*d^2 - (1/2131600)*d*e + (1/2131600)*g^2)*f + (-(1/2131600)*g^2 + (1/2131600)*d*e - (1/2131600)*d^2 + a^2)*g)*(-e + c)^2))/(b*(-g + f)*((f^2 + d^2 - 2*g*f - 2*d*c + c^2 + g^2)*b^2 - 2*a*(-e + c)*(c - d)*b + (-e + c)^2*((1/1460)*f - (1/1460)*g + a)*(-(1/1460)*f + (1/1460)*g + a)))

}

(Gesh it's tiring to reformat these long expressions for the autowrap!)

Best Answer

Related Solutions

MATLAB: Explicit integral could not be found

MATLAB: I need final equation…

Related Question