If \( f(x)=\int_{1}^{x} \frac{\ln t}{1+t} d t \), then....

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If \( f(x)=\int_{1}^{x} \frac{\ln t}{1+t} d t \), then
\( \mathrm{P} \)
(1) \( f\left(\frac{1}{x}\right)=\int_{1}^{x} \frac{\ln t}{(1+t) t} d t \)
(2) \( f\left(\frac{1}{x}\right)=\int_{1}^{x} \frac{t \ln t}{(1+t)} d t \)
(3) \( f(x)+f\left(\frac{1}{x}\right)=x \ln \left(\frac{x}{e}\right) \)
(4) \( f(x)+f\left(\frac{1}{x}\right)=\left(\ln x^{\frac{1}{\sqrt{2}}}\right)^{2} \)


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