求不定积分[x^2/(1+x^2)]arctanxdx
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求不定积分[x^2/(1+x^2)]arctanxdx
![求不定积分[x^2/(1+x^2)]arctanxdx](/uploads/image/z/19521975-39-5.jpg?t=%E6%B1%82%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%5Bx%5E2%2F%281%2Bx%5E2%29%5Darctanxdx)
∫[1-1/(1+x^2)]arctnxdx
=∫arctanxdx-∫arctanxdarctanx
=xarctanx-∫xdx/(1+x^2)-(1/2)(arctanx)^2+C
=xarctanx-(1/2)ln(1+x^2)-(1/2)(arctanx)^2+C
=∫arctanxdx-∫arctanxdarctanx
=xarctanx-∫xdx/(1+x^2)-(1/2)(arctanx)^2+C
=xarctanx-(1/2)ln(1+x^2)-(1/2)(arctanx)^2+C
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