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Problem Calculating Nonlinear Indefinite Integral

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I am trying to calculate a nonlinear integral t^5.2 *exp((-x^6.2-x*(0.2*4.5^6.2))/4.5^6.2) in order to solve an equation, where the unknown is the lower limit of integrations.Although i use "int" in order to calculate the integral, Matlab returns the equation.Is my equation too complicated or there is another way to get a solution ?I am quite new in Matlab, so any help would be appreciated.
I would like to thank you in advance for the time dealing with my query.


darova on 30 Nov 2019
Did you use integral or trapz? What have you tried? Can you elaborate?
Dimitrios Kampitsis
Dimitrios Kampitsis on 1 Dec 2019
My goal is to solve the following equation where the unknown is the limit of integration (k), where a and b are constants
I tried only with int in order to solve the integral and afterwards, if i get a solution from my integration, i am planning to try and solve the equation. However i am not sure if this is the right way to do it.
syms x
g = x^5 *exp((-x^5-x*(4^6))/4^6) ;
I havent tried yet trapz. Moreover i didnt try integral because i am looking for a symbolic solution.
Thanks again.

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Accepted Answer

David Wilson
David Wilson on 2 Dec 2019
Since you neglected to tell us values for a and b, I'll just set them to a=2 and b=1. You have also two definitions for g(x), so I've used the one in your code. Like the previous poster suggested, I'll embed integral inside fsolve:
g = @(x) x.^5.*exp((-x.^5-x*(4^6))/4^6) ;
Q = @(k) integral(g,k,k+2);
a = 2; b = 1; % Set these to whatever
k0 = 1; % Need a start guess here.
k = fsolve(@(k) Q(k) - a/b, k0)

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Dimitrios Kampitsis
Dimitrios Kampitsis on 4 Dec 2019
Thank you for your help, it works and i get a solution. I have tried it also with a more complex equation and it works fine. I really appreciate your help.
However for a specific value of my constants fsolve returns a value (Equation solved) that it is not a root of my equation. I confirmed that using another software "Mathcad".
Could this be a problem of function tolerance ?

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