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Difficult integral?

Hello all,

I'm trying to get the integral with respect to x of the following expression:

(a / x + b(y) * x ^ c) ^ d,

where a,c,d are positive constants, and b is a function of some variable y.

I'm not sure what I'm doing wrong. Can you help me?

I got a solution in Mathematica (some hypergeometric function), but Mathematica is a software that I'm trying not to use anymore.