求∫x2arctanxdx.

admin2022-10-12  27

问题 求∫x2arctanxdx.

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答案∫x2arctanxdx=∫arctancd(x3/3)=x3/3arctanx-1/3∫x3/(1x2)dx=x3arctanx-1/3∫(x-x/(x2+1))dx=x3arctanx-x2/6+1/6ln(1+x2)+C.

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