MATLAB: Integral of a gaussian function wrong answer

integrationintegration gaussian functionsymbolicsymbolic integration

I am trying to calculate the integral of the following Gaussian function:
syms x A
assume(x,'real');
assume(A,'real');
assumeAlso(A>0);
% Expression to integrate
eq = x^14*exp(-x^2/2)*exp(-A*x);
% Integration
ans = int(eq,x,-inf,inf)
Matlab gives me an answer containing hypergeo and erf. However, there is a regular algebraic solution without the needs of hypergeo or erf. (For example type "integral of (x^14*exp(-x^2/2)*exp(-A*x)) from -inf to inf" into wolfram alpha to get algebraic solution)
Is there a way to get to the algebraic answer in Matlab?

Best Answer

I could get the algebraic answer but it required calling "simplify" twice. Need to investigate this further.
>> syms x A
assume(x,'real');
assume(A,'real');
assumeAlso(A>0);
% Expression to integrate
eq = x^14*exp(-x^2/2)*exp(-A*x);
sol = int(eq,x,-Inf,Inf);    % long expression
>> sol1 = simplify(sol,'Steps',500); % first simplify step
>> sol2 = simplify(sol1,'Steps',200) % second simplify step
sol2 =
2^(1/2)*pi^(1/2)*exp(A^2/2)*(A^14 + 91*A^12 + 3003*A^10 + 45045*A^8 + 315315*A^6 + 945945*A^4 + 945945*A^2 + 135135)
Related Question