Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 10

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 10

Answers (1)

best_answer

Answer:

x+\log \left|\frac{x-1}{x+1}\right|+c

Hint:

To solve, this we use partial fraction.

Solution:

\begin{aligned} &I=\int \frac{x^{2}+1}{x^{2}-1} d x \\ &I=\int \frac{(x-1)^{2}+2 x}{x^{2}-1} d x \quad\quad\quad\quad\quad\quad\left[(a-b)^{2}=a^{2}+b^{2}-2 a b\right] \end{aligned}

\begin{aligned} &I=\int \frac{(x-1)^{2}}{x^{2}-1} d x+\int \frac{2 x}{x^{2}-1} d x \\ &I=\int \frac{x-1}{x+1} d x+\int \frac{2 x}{x^{2}-1} d x \end{aligned}

 

\begin{aligned} &I=\int \frac{x+1-2}{x+1} d x+\int \frac{2 x}{x^{2}-1} d x \\ &I=\int d x-2 \int \frac{1}{x+1} d x+\int \frac{2 x}{x^{2}-1} d x \\\ &I=x-2 \log |x+1|+\log \left|x^{2}-1\right|+c \end{aligned}

\begin{aligned} &I=x+\log \left|\frac{x^{2}-1}{(x+1)^{2}}\right|+c \\ &I=x+\log \left|\frac{x-1}{x+1}\right|+c \end{aligned}

 

Posted by

infoexpert27

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 Board Exam Dates 2027 LIVE: CBSE 10th, 12th time table soon; guidelines, changes announced this year
anam-khan

CBSE invites LOC submission for Class 12 re-exams 2026 in West Asian countries
anam-khan

CBSE Datesheet 2027 LIVE: Class 10, 12 board exam timetable soon; sample question papers, marking scheme

Latest Question