Question: Cannot integrate analytically

I have the following function:


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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