I have a curiosity. If
$\int f(x) f'(x)dx=\int f(x) df(x)=\frac{\left(f(x)\right)^{2}}{2}+C$
what is the result of:
$\int f(x) f''(x)dx$
I have a curiosity. If
$\int f(x) f'(x)dx=\int f(x) df(x)=\frac{\left(f(x)\right)^{2}}{2}+C$
what is the result of:
$\int f(x) f''(x)dx$
$ f(x)f'(x)-\int f'(x)^2 \, dx \ ? $
Using by parts $\int f(x)f''(x)dx= f(x)f'(x)-\int f'^2(x)dx$.