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 Class 12th marks uploading for schools in West Asia starts from April 8
anam-khan

CBSE question papers QR codes part of 'internal systems'; board cautions 'unverified claims'
anam-khan

Delhi court grants interim bail to Class 12 student in stabbing case to appear for CBSE exam

Latest Question