From the documentation on DSolve:
Solutions given by DSolve sometimes include integrals that cannot be
carried out explicitly by Integrate. Variables K[1], K[2],
... are used in such integrals.
Here's a simple example which produces output with an integral:
DSolve[y'[x] == f[x], y, x]
{{y -> Function[{x}, C[1] + Integrate[f[K[1]], {K[1], 1, x}]]}}
There's no way to just get rid of the integral. It has to exist in this output.
Do you believe that the integral it gives should be evaluatable? If so, what is the integral? Maybe the integral is evaluatable under some kind of assumption like "C[1] is a positive real number". If that's the case, you might be able to use FullSimplify and Assumptions to get your answer. If not, then the Integral is an inherent part of the symbolic solution.