polynomial 多项式
Basically, there are two types of indefinite integral.
One is polynomial
, which composed by + and −
Another is composite function
, which composed by × and ÷
For the first type of integral, we use basic formula to each part of it directly:
==∫x3x2−2x+1dx∫(3x−2+x1)dx23x2−2x+ln∣x∣+C For the second one, oh my god, it's very complicate.
Here's a basic template:
∫f(g(x))⋅g′(x)dx∫f(g(x))⋅dg(x)∫f(u)⋅du Let's do some exercise:
====∫xe−x2⋅dx∫e−x2⋅xdx(−21)∫e−x2⋅(−2)xdx(−21)∫e−x2⋅d(−x2)(−21)e−x2+C//composite function in front//find a way to make x = (−x2)′=−2x while keeping equation’s balance//we knew g′(x)dx=dg(x)//see −x2 as a part, then apply basic integral formula