(1+x^2)^2分之(1-x^2)求积分,
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(1+x^2)^2分之(1-x^2)求积分,
![(1+x^2)^2分之(1-x^2)求积分,](/uploads/image/z/19065867-51-7.jpg?t=%281%2Bx%5E2%29%5E2%E5%88%86%E4%B9%8B%281-x%5E2%29%E6%B1%82%E7%A7%AF%E5%88%86%2C)
∫(1-x^2)/(1+x^2)^2 dx
= -∫(1-1/x^2)/(x+1/x)^2 dx
= -∫ 1/(x+1/x)^2 [ (1-1/x^2)dx]
= -∫ 1/(x+1/x)^2 d(x+1/x)
= 1/(x+1/x) +C
= x/(x^2+1) +C
= -∫(1-1/x^2)/(x+1/x)^2 dx
= -∫ 1/(x+1/x)^2 [ (1-1/x^2)dx]
= -∫ 1/(x+1/x)^2 d(x+1/x)
= 1/(x+1/x) +C
= x/(x^2+1) +C