求不定积分∫xarctanxdx

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求不定积分∫xarctanxdx求不定积分∫xarctanxdx求不定积分∫xarctanxdx∫x*arctanxdx=∫arctanxd(x²/2)=(x²/2)arctanx

求不定积分∫xarctanxdx
求不定积分∫xarctanxdx

求不定积分∫xarctanxdx
∫ x * arctanx dx
= ∫ arctanx d(x²/2)
= (x²/2)arctanx - (1/2)∫ x² d(arctanx)
= (x²/2)arctanx - (1/2)∫ x²/(x² + 1) dx
= (x²/2)arctanx - (1/2)∫ (x² + 1 - 1)/(x² + 1) dx
= (x²/2)arctanx - (1/2)∫ dx + (1/2)∫ dx/(x² + 1)
= (x²/2)arctanx - x/2 + (1/2)arctanx + C