Question: Cannot integrate analytically

I have the following function:

f:=t->862.979774+1825.011621/([1+1.54943476*e^(-677.0138344*t)]^(131537/203808))

Is there any way Maple can calculate the indefinite integral of f(t)? I have tried integrating f(t) in a range t=tmin..tmax numerically using dsolve/numeric and plotting the numeric integral and I am satisfied with the result, but I would much prefer an analytic integration so that I obtain some function y(t) that I can later use which will be the indefinite integral of f(t).

So far, I have tried unsuccessfully to obtain an indefinite integral of f(t) using int and dsolve. Thanks in advance.

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