∫x2arctanxdx=________.

admin2021-10-18  43

问题 ∫x2arctanxdx=________.

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答案x3/3arctanx-x2/6+1/6ln(1+x2)+C

解析 ∫x2arctanxdx=1/3∫arctanxd(x3)-x3/3arctanx-1/3∫x3/(1+x2)dx=x3/3arctanx-1/3∫(x-x/1+x2)dx=x3/3arctanx-x2/6+1/6ln(1+x2)+C.
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