设f(x)当X>0时连续∫f(x)dx=2x/(1+x^2)+C,求f(x)
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设f(x)当X>0时连续∫f(x)dx=2x/(1+x^2)+C,求f(x)
∫f(x)dx=2x/(1+x²)+C
f(x)=d/dx [2x/(1+x²)+C],对右边进行微分
=2*d/dx[x/(1+x²)]
=2*1/(1+x²)²*[(1+x²)*1-x*(0+2x)]
=2/(1+x²)²*(1+x²-2x²)
=2(1-x²)/(1+x²)²
f(x)=d/dx [2x/(1+x²)+C],对右边进行微分
=2*d/dx[x/(1+x²)]
=2*1/(1+x²)²*[(1+x²)*1-x*(0+2x)]
=2/(1+x²)²*(1+x²-2x²)
=2(1-x²)/(1+x²)²
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