求不定积分(1+2x^2)/[x^2*(1+x^2)]dx,
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![求不定积分(1+2x^2)/[x^2*(1+x^2)]dx,](/uploads/image/z/1633019-59-9.jpg?t=%E6%B1%82%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%281%2B2x%5E2%29%2F%5Bx%5E2%2A%281%2Bx%5E2%29%5Ddx%2C)
求不定积分(1+2x^2)/[x^2*(1+x^2)]dx,
求不定积分(1+2x^2)/[x^2*(1+x^2)]dx,
求不定积分(1+2x^2)/[x^2*(1+x^2)]dx,
∫ (1+2x²)/[x²(1+x²)] dx
=∫ [(1/x²)+1/(1+x²)]dx
=∫ (1/x²) dx+∫ 1/(1+x²) dx
=-1/x+arctanx+C
C为任意常数
∫(1+2x^2)/[x^2*(1+x^2)]dx
=∫(1+x^2+x²)/[x^2*(1+x^2)]dx
=∫(1/(1+x^2)+1/[x^2]dx
=arctanx-1/x+c
dx?
目测吧 孩子!!!