∫1/x²(x²+1)dx
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∫1/x²(x²+1)dx
∫1/x²(x²+1)dx
∫1/x²(x²+1)dx
∫1/x²(1+x²)dx
=∫(1+x²-x²)/x²(1+x²)dx
=∫(1+x²)/x²(1+x²)dx-∫x²/x²(1+x²)dx
=∫1/x²dx-∫1/(1+x²)dx
=-1/x-arctanx+C