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∫x²/(1+x²)²dx
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∫1/(1+X²)²dx
解:∫1/(1+X²)²dx=∫(1+x²-1)/(1+X²)²dx=∫1/(1+X²)dx-∫x²/(1+X²)²dx=
arctanx+1/2∫xd1/(1+X²)=arctanx+1/2(x/(1+x²)-∫1/(1+X²)dx)=1/2arctanx+x/(2(x²+1))+C
解:∫1/(1+X²)²dx=∫(1+x²-1)/(1+X²)²dx=∫1/(1+X²)dx-∫x²/(1+X²)²dx=
arctanx+1/2∫xd1/(1+X²)=arctanx+1/2(x/(1+x²)-∫1/(1+X²)dx)=1/2arctanx+x/(2(x²+1))+C
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