求下列不定积分,∫xarctanxdx

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求下列不定积分,∫xarctanxdx求下列不定积分,∫xarctanxdx求下列不定积分,∫xarctanxdx∫xarctanxdx=(1/2)∫arctanxd(x^2)=(1/2)x^2·ar

求下列不定积分,∫xarctanxdx
求下列不定积分,∫xarctanxdx

求下列不定积分,∫xarctanxdx
∫xarctanxdx
=(1/2)∫arctanxd(x^2)
=(1/2)x^2·arctanx-(1/2)∫x^2d(arctanx)
=(1/2)x^2·arctanx-(1/2)∫[x^2/(1+x^2)]dx
=(1/2)x^2·arctanx-(1/2)∫dx+(1/2)∫[1/(1+x^2)]dx
=(1/2)x^2·arctanx-(1/2)x+(1/2)arctanx+C