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 Indefinite Integrals Excercise Very Short Answers Question 17

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 17

Answers (1)

best_answer

Answer: \frac{\left(\tan ^{-1} x\right)^{4}}{4}+c

Hint: You must know about the integral rule of tangent function.

Given: \int \frac{\left ( \tan^{-1} x\right )^{3}}{1+x^{2}}dx

Solution:  

I=\int \frac{\left ( \tan^{-1} x\right )^{3}}{1+x^{2}}dx

Let \tan^{-1}x=t and differentiate both sides,

                        \frac{1}{1+x^{2}}dx=dt                                                                  \left [ \frac{d}{dt} \tan^{-1}x=\frac{1}{1+x^{2}}\right ]

                \begin{aligned} &I=\int\left(t^{3}\right) d t \\ &=\frac{t^{4}}{4}+c \\ &{\left[\int x^{n} d x=\frac{x^{n+1}}{n+1}+c\right]} \\ &=\frac{\left(\tan ^{-1} x\right)^{4}}{4}+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 Class 10, 12 board exams 2025 from April 7 to 11 for sports students
anam-khan

CBSE Class 12 history paper 2025 moderately difficult, tested students’ understanding
anam-khan

CBSE Class 12 Computer Science Exam Analysis 2025: Paper 'moderate', but 'tougher' than last three years

Latest Question