Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 35 Maths Textbbok Solution.

Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise  Revision Exercise Question 35 Maths Textbbok Solution.

Answers (1)

Answer:

\frac{1}{2}\left|\log \left(1+x^{2}\right)\right|+\frac{1}{2\left(1+x^{2}\right)}+c

Given:

\int \frac{x^{3}}{\left(1+x^{2}\right)^{2}} d x

Hint:

To solve the statement we will suppose x in term of t.

Solution: 

\int \frac{x^{2} x}{\left(1+x^{2}\right)^{2}} d x

Let 1+x^{2}=t

2 x=\frac{d t}{d x}

x d x=\frac{d t}{2}

I=\frac{1}{2} \int \frac{t-1}{t^{2}} d t

I=\frac{1}{2} \int \frac{t}{t^{2}} d t-\int \frac{1}{t^{2}} d t

I=\frac{1}{2} \int \frac{1}{t} d t-\int t^{-2} d t

I=\frac{1}{2} \log t-\frac{1}{2} \frac{\left(t^{-2+1}\right)}{-2+1}+c

I=\frac{1}{2}\left|\log \left(1+x^{2}\right)\right|+\frac{1}{2\left(1+x^{2}\right)}+c

Posted by

infoexpert21

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 Exams 2027 LIVE: Class 12, 10 exam dates soon; LOC submission, passing marks
anam-khan

CBSE organises webinar on LOC registration, correction queries for Class 10, 12 board exam 2027
anam-khan

CBSE Board Exam Date 2027 Highlights: Class 10, 12 exam schedule soon at cbse.gov.in

Latest Question