Integrating the density function of Brownian motion

I am going to find the integral

for some nice enough function f. The integrand has a very strong singularity at t=0. the function integral2 gives me warning so often. Do we have some good function for an ancurate answer?

Answer 1

[Torsten]

Maybe it helps to resolve the integration with respect to t:

syms t T real positive
syms x real
g = 1/sqrt(t)*exp(-x^2/t);
int(g,t,0,T)

ans = 

[ho man]

I am so sorry to forget to make f depends on t also, which is f(x,t) instead of f(x), is there any solution for this?

[Torsten]

Ok, after you changed f(x) to f(x,t), the answer is no longer relevant (at least if f cannot be split in f1(t)*f2(x)).