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∫xArCtAnxDx

∫xarctanxdx =(1/2)∫ arctanxd(x²) 那么使用分部积分法得到, =(1/2)x²arctanx - (1/2)∫ x²/(1+x²) dx =(1/2)x²arctanx - (1/2)∫ (x²+1-1)/(1+x²) dx =(1/2)x²arctanx - (1/2)∫ 1 dx + (1/2)∫ 1/(1+x&#...

分部积分思想: ∫x^2arctanxdx=(1/3)∫arctanxdx^3 =(1/3)x^3arctanx-(1/3)∫x^3darctanx =(1/3)x^3arctanx-(1/3)∫[(x^3+x)-x]/(1+x^2)dx =(1/3)x^3arctanx-(1/3)∫xdx+(1/3)∫(x)/(1+x^2)dx =(1/3)x^3arctanx-(1/6)x^2+(1/6)ln(1+x^2)+C(C为常数)...

∫xarctanxdx =∫arctanxdx²/2 =x²/2arctanx-∫x²/2darctanx =x²/2arctanx-1/2∫x²/(1+x²)dx =x²/2arctanx-1/2∫(x²+1-1)/(1+x²)dx ==x²/2arctanx-1/2∫1-1/(1+x²)dx ==x²/2arctanx-1/2x...

∫ x²arctanx dx = ∫ arctanx d(x³/3) = (1/3)x³arctanx - (1/3)∫ x³ d(arctanx) = (1/3)x³arctanx - (1/3)∫ x³/(1 + x²) dx = (1/3)x³arctanx - (1/3)∫ x[(1 + x²) - 1]/(1 + x²) dx = (1/3)...

用分部积分法, ∫ x² arctanx dx =1/3 ∫ arctanx d(x³) =1/3 x³ arctanx - 1/3 ∫x³/(1+x²) dx =.......后面会了吧

∫xarctanxdx =1/2∫arctanxdx² =1/2x²arctanx-1/2∫x²/(1+x²)dx =1/2x²arctanx-1/2∫[1-1/(1+x²)]dx =1/2x²arctanx-1/2x+1/2arctanx+c

xarctanx

原式=-∫arctanxd(1/x) =-(arctanx)/x+∫1/[x(1+x^2)]dx =-(arctanx)/x+∫1/x-x/(1+x^2)dx =-(arctanx)/x+lnlxl-1/2lnlx^2+1l+C

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