积分:x乘arctanx dx
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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