求下列不定积分,∫xarctanxdx

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/15 05:49:25
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