Question

求原函数中用到个公式看不懂 后面是个一阶导数

Answer 1

右边={∫_0^x[xf(t)]dt}'-{∫_0^x[tf(t)]dt}'

={x∫_0^x[f(t)]dt}'-{∫_0^x[tf(t)]dt}' (注意t是积分变量,x在积分中看作常量）

=∫_0^x[f(t)]dt+xf(x)-xf(x)

=∫_0^x[f(t)]dt=左边,