Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • 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}

Posted by

infoexpert26

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 12 Board Exam 2026 LIVE: 12th English paper ends; answer key, analysis
anam-khan

QR code in CBSE Class 12 maths paper redirects to 'rickroll' prank video; board says exam integrity intact
anam-khan

Iran-Israel Conflict: CBSE postpones Class 12 board exams 2026 till March 16 in Middle East

Latest Question