Question

链式法则反积分

关于积分代换法有疑问
反推链式法则有∫ f‘(g(x))g'(x)dx=f(g(x))+C,此时用u和du代换掉g(x)和g'(x)dx,请问那前后的f’和f到哪去了

Answer 1

∫ f‘(g(x))g'(x)dx
let u = g(x)
du = g'(x) dx
∫ f‘(g(x))g'(x)dx
=∫ f‘(u)du
= f(u) + C
=f(g(x)) + C