In(1+X^2)/X^4不定积分答案是1/3X - In(1+X^2)/3X^3 -2/3arctanX

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/19 04:08:04

In(1+X^2)/X^4不定积分答案是1/3X - In(1+X^2)/3X^3 -2/3arctanX
In(1+X^2)/X^4不定积分
答案是1/3X - In(1+X^2)/3X^3 -2/3arctanX

In(1+X^2)/X^4不定积分答案是1/3X - In(1+X^2)/3X^3 -2/3arctanX
由分步积分得∫In(1+x^2)dx/x^4
=-In(1+x^2)/3x^3+∫(dx/3x^3)*[2x/(1+x^2)]
=-In(1+x^2)/3x^3+(2/3)∫dx/[x^2(1+x^2)]
=-In(1+x^2)/3x^3+(2/3)∫[1/x^2-1/(x^2+1)]dx
=-In(1+x^2)/3x^3-2/3x-(2/3)arctanx+C