求不定积分x^2arctanxdx
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原式=arctanx*x^3/3-∫x^3/3d(arctanx)
=arctanx*x^3/3-(1/3)∫(x^3/(x^2+1))dx
=arctanx*x^3/3-(1/3)∫(x-x/(x^2+1))dx
=arctanx*x^3/3-(1/3)∫xdx+(1/6)∫d(x^2+1)/(x^2+1)
=arctanx*x^3/3-x^2/6+(1/6)ln|x^2+1|+C
=arctanx*x^3/3-(1/3)∫(x^3/(x^2+1))dx
=arctanx*x^3/3-(1/3)∫(x-x/(x^2+1))dx
=arctanx*x^3/3-(1/3)∫xdx+(1/6)∫d(x^2+1)/(x^2+1)
=arctanx*x^3/3-x^2/6+(1/6)ln|x^2+1|+C
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