求不定积分∫x arctanxdx

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求不定积分∫x arctanxdx

∫x arctanxdx
=1/2∫ arctanxdx^2
=x^2arctanx/2-1/2∫x^2darctanx
=x^2arctanx/2-1/2∫x^2/(1+x^2)dx
=x^2arctanx/2-1/2∫(1-1/(1+x^2))dx
=x^2arctanx/2-x/2+arctanx/2+C.