搜搜做题作业网(x^4+1)/[x^2(x^2+1)]的积分
来源：学生作业帮 编辑：搜搜做题作业网作业帮 分类：数学作业 时间：2024/06/30 11:24:59
(x^4+1)/[x^2(x^2+1)]的积分
![(x^4+1)/[x^2(x^2+1)]的积分](/uploads/image/z/15785493-69-3.jpg?t=%28x%5E4%2B1%29%2F%5Bx%5E2%28x%5E2%2B1%29%5D%E7%9A%84%E7%A7%AF%E5%88%86)
(x^4+1)/(x^2(x^2+1)=A/x^2+(Bx^2+C)/(x^2+1)
Ax^2+A+Bx^4+Cx^2=x^4+1
B=1,A+C=0,A=1
所以C=-1
f(x)=(x^4+1)/(x^2(x^2+1))=1/x^2+(x^2-1)/(x^2+1)
∫f(x)dx
=-1/x+∫[1-2/(x^2+1)]dx
=-1/x+x-2arctanx
Ax^2+A+Bx^4+Cx^2=x^4+1
B=1,A+C=0,A=1
所以C=-1
f(x)=(x^4+1)/(x^2(x^2+1))=1/x^2+(x^2-1)/(x^2+1)
∫f(x)dx
=-1/x+∫[1-2/(x^2+1)]dx
=-1/x+x-2arctanx