Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • provide solution for RD Sharma maths class 12 chapter indefinite integrals exercise 18.1 question 3

provide solution for RD Sharma maths class 12 chapter indefinite integrals exercise 18.1 question 3

Answers (1)

Answer: \frac{x^{3}}{3}+c

Hint: Use the formulas of logarithm

Given:\int \frac{e^{6\log_{e}x}-e^{5\log_{e}x}}{e^{4\log_{e}x}-e^{3\log_{e}x}}dx

Solution:\int \frac{e^{6\log_{e}x}-e^{5\log_{e}x}}{e^{4\log_{e}x}-e^{3\log_{e}x}}dx

=\int \int \frac{e^{\log_{e}x^{6}}-e^{\log_{e}x^{5}}}{e^{\log_{e}x^{4}}-e^{\log_{e}x^{3}}}dx                                        \left ( \because x\log_{e}x=\log_{e}x^{x} \right )

=\int \frac{x^{6}-x^{5}}{x^{4}-x^{3}}dx=\int \frac{x^{5}(x-1)}{x^{3}(x-1)}dx                            \left ( \because e^{\log e^{x}}=x \right )

=\int \frac{x^{5}}{x^{3}}dx=\int x^{2}dx

=\frac{x^{3}}{3}+c

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 Hindi exam 2025 not postponed; special exam for those who miss
anam-khan

CBSE Class 12 English Exam Analysis 2025: Paper rated 'easy, straightforward'; section-wise difficulty level
anam-khan

CBSE 12th Board Exam Live: CBSE Class 12 English paper 'easy and balanced'; answer key updates

Latest Question