อ้างอิง:
ข้อความเดิมเขียนโดยคุณ -InnoXenT-
38. $$\int_{e}^{e^2} \frac{1+(\ln{x})(\ln{(\ln{x})})}{\ln{x}}\, dx$$
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\[
\int\limits_e^{e^2 } {\frac{{1 + \left( {\ln x} \right)\left( {\ln \left( {\ln x} \right)} \right)}}{{\ln x}}} dx = \int\limits_e^{e^2 } {\frac{1}{{\ln x}}} dx + \int\limits_e^{e^2 } {\ln \left( {\ln x} \right)} dx = \int\limits_e^{e^2 } {\frac{1}{{\ln x}}} dx + \left[ {x\ln \left( {\ln x} \right)} \right]_e^{e^2 } - \int\limits_e^{e^2 } {\frac{1}{{\ln x}}} dx = e^2 \ln 2
\]