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  • Explain solution RD Sharma class 12 chapter 19 Definite Integrals exercise Fill in the blanks question 8 maths

Explain solution RD Sharma class 12 chapter 19 Definite Integrals exercise Fill in the blanks question 8 maths

Answers (1)

Answer: e^{e}

Hint:Using \int e^{x}\left(f(x)+f^{\prime}(x)\right) d x

Given: \int_{1}^{e} \frac{e^{x}}{x}(1+\log x) d x

Solution:  

\begin{aligned} \mathrm{I} &=\int_{1}^{e} e^{x}\left(\frac{1}{x}+\log x\right) d x \\\\ &=\int_{1}^{e} e^{x}\left(\frac{1}{x}+\log x\right) d x \end{aligned}

    \begin{aligned} &=\left[e^{x} \log x\right]_{1}^{e} \ldots \ldots \int e^{x}\left(f(x)+f^{\prime}(x)\right) d x=e^{x} f(x) \\\\ &=e^{e} l o g e-e^{1} \log 1 \\\\ &=e^{e} \quad \ldots[\because \log e=1 ; \log 1=0] \end{aligned}

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