用分部积分法求 X · arctanx 的不定积分
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x arctanx dx
= arctanx d(x²/2)
= (x²/2)arctanx - (1/2)x² d(arctanx)
= (1/2)x²arctanx - (1/2)x²/(x² + 1) dx
= (1/2)x²arctanx - (1/2)∫ [(x² + 1) - 1]/(x² + 1) dx
= (1/2)x²arctanx - (1/2)∫ dx + (1/2)∫ dx/(x² + 1)
= (1/2)x²arctanx - x/2 + (1/2)arctanx + C
咨询记录 · 回答于2022-01-05
用分部积分法求 X · arctanx 的不定积分
x arctanx dx= arctanx d(x²/2)= (x²/2)arctanx - (1/2)x² d(arctanx)= (1/2)x²arctanx - (1/2)x²/(x² + 1) dx= (1/2)x²arctanx - (1/2)∫ [(x² + 1) - 1]/(x² + 1) dx= (1/2)x²arctanx - (1/2)∫ dx + (1/2)∫ dx/(x² + 1)= (1/2)x²arctanx - x/2 + (1/2)arctanx + C
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