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Solve the rational integral $$\int_1^x \frac{1}{t^{2023}-t^{2022}+t^{2021}-t^{2020}} dt.$$

I am trying to solve a IVP and this is the last step to solving it, but I can't get through it. I tried the ordinary method of trying to separate them into fractions. The factorization is $t^{2020}(t^2+1)(t-1)$. With no success.

Gary
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Csaba Daniel Farkaš
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    The integral does not converge, the integrand behaves like $\frac{1}{2(t-1)}$ near $t=1$. – Gary Jun 30 '23 at 07:30

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