Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Please solve RD Sharma class 12 chapter Indefinite Integrals exercise 18.9 question 21 maths textbook solution

Please solve RD Sharma class 12 chapter Indefinite Integrals exercise 18.9 question 21 maths textbook solution

Answers (1)

Answer:  \frac{4}{3}\left(x^{2}+x+1\right)^{\frac{3}{2}}+c

Hint: Use substitution method to solve this integral.

Given: \int(4 x+2) \sqrt{x^{2}+x+1} d x

Solution:

        \begin{aligned} &\text { Let } I=\int(4 x+2) \sqrt{x^{2}+x+1} d x \\ &\Rightarrow I=2 \int(2 x+1) \sqrt{x^{2}+x+1} d x \\ &\text { Put } x^{2}+x+1=t \Rightarrow(2 x+1) d x=d t \text { then } \end{aligned}

        I=2 \int(2 x+1) \sqrt{t} \cdot \frac{d t}{(2 x+1)}=2 \int \sqrt{t} d t

        =2 \int t^{\frac{1}{2}} d t=2\left[\frac{t_{2}^{\frac{1}{+1}}}{\frac{1}{2}+1}\right]+\mathrm{c} \quad\left[\because \int x^{n} d x=\frac{x^{n+1}}{n+1}+c\right]

        =2\left[\frac{t^{\frac{3}{2}}}{\frac{3}{2}}\right]+\mathrm{C}=2 \cdot \frac{2}{3} t^{\frac{3}{2}}+c

        =\frac{4}{3}\left(x^{2}+x+1\right)^{\frac{3}{2}}+c \quad\left[\because t=x^{2}+x+1\right]

Posted by

infoexpert26

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 announces STEM education as annual training theme for 2025
anam-khan

Board Exam 2025 Admit Card LIVE: WBBSE, UPMSP hall tickets soon; updates on other state boards admit cards
anam-khan

CBSE Class 10, 12 admit card 2025 out for regular, private students at Pariksha Sangam portal

Latest Question