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 extends single girl child scholarship registration deadline till November 20

Latest Question