I am trying to find an analytical soltuion to the integral
I= int(exp(-x)*P(x)/Q(x),x,0,inf)
where P and Q are both polynnomials and P/Q is bounded at infinity. An example is:
syms a x int(x*exp(-a*x)/(x^2+1),x,[0 inf])
This gives:
piecewise(angle(a) in Dom::Interval([-pi/2], [pi/2]) & a ~= 0, (2*meijerG([-1/2, 0, 0], [], 0, [], 4/a^2))/(a^2*pi^(1/2)), ~angle(a) in Dom::Interval([-pi/2], [pi/2]) | a == 0, int((x*exp(-x*a))/(x^2 + 1), x, 0, Inf))
This is just one example but am I doing something wrong here or is the Symbolic Toolbox limited in this respect?
Best Answer