积分：x乘arctanx dx

积分：x乘arctanx dx
积分：x乘arctanx dx

积分：x乘arctanx dx
分部积分
x * arctanx dx = arctanx d（x^2 /2)
∫x * arctanx dx = ∫arctanx d（x^2 /2)
= arctanx（x^2 /2) – (1/2)∫x^2 / (1+x^2) dx
∫x^2 / (1+x^2) dx = x – arctanx + C
∴∫x * arctanx dx =（x^2+1）arctanx / 2 – x/2 +C

(arctan[x] + x^2 arctan[x]-x)/2

先用换元法,再用分部积分.
1/2(arctan(x)*x^2-x+arctan(x))+C