∫x² arctanx dx
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∫ x² arctanx dx
= ∫ arctanx d(x³/3)
= (x³/3) arctanx - ∫ (x³/3) d[arctanx]
= (1/3)x³ arctanx - (1/3)∫ [x³][1/(1+x²)] dx
= (1/3)x³ arctanx - (1/3)∫ x(x²+1-1)/(1+x²) dx,加一减一法
= (1/3)x³ arctanx - (1/3)∫ [x - x/(1+x²)] dx
= (1/3)x³ arctanx - (1/3)[(x²/2) - (1/2)ln(1+x²)] + C
= (1/3)x³ arctanx - (x²/6) + (1/6)ln(1+x²) + C
= ∫ arctanx d(x³/3)
= (x³/3) arctanx - ∫ (x³/3) d[arctanx]
= (1/3)x³ arctanx - (1/3)∫ [x³][1/(1+x²)] dx
= (1/3)x³ arctanx - (1/3)∫ x(x²+1-1)/(1+x²) dx,加一减一法
= (1/3)x³ arctanx - (1/3)∫ [x - x/(1+x²)] dx
= (1/3)x³ arctanx - (1/3)[(x²/2) - (1/2)ln(1+x²)] + C
= (1/3)x³ arctanx - (x²/6) + (1/6)ln(1+x²) + C
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