Question

integral of f(x). f'(x) dx

Answer 1

$\int \: f(x). {f}^{'} (x) \: dx \\ put \: \: f(x) = u \\ then \: \: {f}^{'} (x) \: dx = du \\ integral \: \: becomes \\ \int \: u \: du = \frac{ {u}^{2} }{2} + c = \frac{ {(f(x))}^{2} }{2} + c$