<s>[INST] The integral of $x^3/(x^2+4x+3)$ I'm stumped in solving this problem. Every time I integrate by first dividing the $x^3$ by $x^2+4x+3$ and then integrating $x- \frac{4x^2-3}{x+3)(x+1)}$ using partial fractions, I keep getting the wrong answer. 
 [/INST] $$\frac{2x^3}{(x+1)(x+3)}=\frac{[(x+3)-(x+1)]x^3}{(x+1)(x+3)}=\frac{x^3}{x+1}-\frac{x^3}{x+3}$$
For $\displaystyle\int\dfrac{x^3}{x+a}dx,$ set $x+a=h$
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