Question

有理函数得积分问题？

如图所示为什么划线部分可以变成（x-1）^2

Answer 1

∫ dx/(x-1)
=∫ d(x-1)/(x-1)
=ln|x-1| +C
∫(x-1)/(x^2+1) dx
=∫x/(x^2+1) dx -∫dx/(x^2+1)
=(1/2)∫d(x^2+1)/(x^2+1) -∫dx/(x^2+1)
=(1/2)ln|x^2+1| -arctanx + C