5
$\begingroup$

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:

$\int f(x) f''(x)dx$

  • 0
    @Mathlover, that's a nice observation, thanks.2012-07-04

2 Answers 2

2

$ f(x)f'(x)-\int f'(x)^2 \, dx \ ? $

  • 4
    @draks What is math.stackexchange?2012-07-04
2

Using by parts $\int f(x)f''(x)dx= f(x)f'(x)-\int f'^2(x)dx$.