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Answer
$$ \displaystyle\int \dfrac{4x+5}{\left(x-1\right){\cdot}{\left(x+2\right)}^{2}}\, \mathrm d x = -{{x\,\ln \left(x+2\right)+2\,\ln \left(x+2\right)-\ln \left(x-1 \right)\,x-2\,\ln \left(x-1\right)+1}\over{x+2}} $$
Explanation
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