<s>[INST] Computing $\int \frac{6x}{\sqrt{x^2+4x+8}} dx$ I am trying to compute an indefinite integral. Thanks!
$$\int \frac{6x}{\sqrt{x^2+4x+8}} dx.$$
 [/INST] $$
\begin{align}
\int \frac{6x +12 -12}{\sqrt{x^2+4x+8}} dx
  &= \int \frac{6x +12}{\sqrt{x^2+4x+8}} dx - \int \frac{12}{\sqrt{x^2+4x+8}} dx \\
  &= \int \frac{6(x+2)}{\sqrt{x^2+4x+8}} dx - \int \frac{12}{\sqrt{x^2+4x+8}} dx \\ 
  &= \int \frac{3(2x+4)}{\sqrt{x^2+4x+8}} dx - \int \frac{12}{\sqrt{x^2+4x+8}} dx.
\end{align}$$
Then take 
$x^2+4x+8 = t$ substitution in 1st integral and performed perfect polynomial in second integral then simplify to get the answer.
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