<s>[INST] Solve $\int\frac{8x+9}{(2x+1)^3}\,dx$. Do I split  $\displaystyle\int\frac{8x+9}{(2x+1)^3}\,dx$  into partial fractions? Or do I use $(2x+1)^{-3}$ by itself? Not sure what to do. Please advice. 
The answer given is $\dfrac{-16x+13}{4(2x+1)^2} +C$
 [/INST] write the numerator of the integrand as $$8x+4+5=4(2x+1)+5$$ then we have 
$$4\int\frac{dx}{(2x+1)^2}dx+5\int\frac{dx}{(2x+1)^3}dx$$ now you can set $$u=2x+1$$ and proceed.
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