∫[1/(4-x^2)x^2]dx
答案:1 悬赏:80
解决时间 2021-01-10 14:18
- 提问者网友：欲劫无渡
- 2021-01-09 21:51
∫[1/(4-x^2)x^2]dx
最佳答案
- 二级知识专家网友：鸠书
- 2021-01-09 22:23
原式=(1/4)∫[1/(4-x²)+(1/x²)]dx
=(1/4)[-∫1/(x²-4)]dx+∫(1/x²)dx]
=(-1/16)∫[1/(x-2)-1/(x+2)]dx-(1/4)*(1/x)
=(-1/16)ln|(x-2)/(x+2)|-(1/4)*(1/x)+C
=(1/4)[-∫1/(x²-4)]dx+∫(1/x²)dx]
=(-1/16)∫[1/(x-2)-1/(x+2)]dx-(1/4)*(1/x)
=(-1/16)ln|(x-2)/(x+2)|-(1/4)*(1/x)+C
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