∫(arctanx)²dx＝
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解决时间 2021-01-03 10:58
- 提问者网友：焚苦与心
- 2021-01-03 03:03
∫(arctanx)²dx＝
最佳答案
- 五星知识达人网友：洒脱疯子
- 2021-01-07 01:02
∫x(arctanx)²dx
=1/2∫(arctanx)²dx²
=1/2(xarctanx)²-∫(x²arctanx)/(1+x²)dx
=1/2(xarctanx)²-∫[arctanx-arctanx/(1+x²)]dx
=1/2(xarctanx)²-∫arctanxdx-∫arctanxd(arctanx)
=1/2(xarctanx)²-xarctanx+∫x/(1+x²)dx-1/2(arctanx)²
=1/2(xarctanx)²-xarctanx+1/2ln(1+x²)-1/2(arctanx)²+C
=1/2∫(arctanx)²dx²
=1/2(xarctanx)²-∫(x²arctanx)/(1+x²)dx
=1/2(xarctanx)²-∫[arctanx-arctanx/(1+x²)]dx
=1/2(xarctanx)²-∫arctanxdx-∫arctanxd(arctanx)
=1/2(xarctanx)²-xarctanx+∫x/(1+x²)dx-1/2(arctanx)²
=1/2(xarctanx)²-xarctanx+1/2ln(1+x²)-1/2(arctanx)²+C
全部回答
- 1楼网友：迟山
- 2021-01-07 02:05
d(arctanx)=1/(x^2+1)dx,所以∫(arctanx)^2dx=[(1+x^2)(arctanx)^3/3]+c
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