Indefinite integral?

$\int {\frac{{1 + \sqrt {2s - 1} }} {{\sqrt {2s - 1} }}} ds = \int {1 + } \frac{1} {{\sqrt {2s - 1} }}ds = s + \left( {2s - 1} \right)^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$2$}}} + C$

The answer is given in an equivalent form:

$0.5\left( {1 + \sqrt {2s - 1} } \right)^2 = 0.5\left( {1 + 2\sqrt {2s - 1} + 2s - 1} \right) = \sqrt {2s - 1} + s $

Quote:

(x²+3)^7 (x³-8x) dx

I'm not sure how to understand this?