<s>[INST] Calculus simplification Could someone explain how this:
$\int(\frac{x}{\sqrt{x+1}})dx$ 
becomes:
$\int(\sqrt{x+1})dx - \int(\frac{1}{\sqrt{x+1}})dx$
 [/INST] It’s got nothing to do with the integral:
$$\begin{align}
\frac{x}{\sqrt{x+1}} &= \frac{x+1-1}{\sqrt{x+1}}\\
&= \frac{x+1}{\sqrt{x+1}} - \frac{1}{\sqrt{x+1}}\\
&= \sqrt{x+1} - \frac{1}{\sqrt{x+1}}
\end{align}$$
Does that help?
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