作业帮求不定积分(1+2x^2)/[x^2*(1+x^2)]dx为什么直接变成了 ∫[1/x²+1/(1+x²)]dx 1+2x^2 哪里去了?
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![求不定积分(1+2x^2)/[x^2*(1+x^2)]dx为什么直接变成了 ∫[1/x²+1/(1+x²)]dx 1+2x^2 哪里去了?](/uploads/image/z/3762849-57-9.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%E4%B8%BA%E4%BB%80%E4%B9%88%E7%9B%B4%E6%8E%A5%E5%8F%98%E6%88%90%E4%BA%86+%E2%88%AB%5B1%2Fx%26%23178%3B%2B1%2F%281%2Bx%26%23178%3B%29%5Ddx+1%2B2x%5E2+%E5%93%AA%E9%87%8C%E5%8E%BB%E4%BA%86%3F)
求不定积分(1+2x^2)/[x^2*(1+x^2)]dx为什么直接变成了 ∫[1/x²+1/(1+x²)]dx 1+2x^2 哪里去了?
求不定积分(1+2x^2)/[x^2*(1+x^2)]dx
为什么直接变成了 ∫[1/x²+1/(1+x²)]dx 1+2x^2 哪里去了?
求不定积分(1+2x^2)/[x^2*(1+x^2)]dx为什么直接变成了 ∫[1/x²+1/(1+x²)]dx 1+2x^2 哪里去了?
(1+2x^2)/[x^2*(1+x^2)]
=(1+x^2+x^2)/[x^2*(1+x^2)]
=(1+x^2)/[x^2*(1+x^2)]+x^2/[x^2*(1+x^2)]
=1/x^2+1/(1+x^2)
所以原式=-1/x+arctanx+C