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 18 Indefinite Integrals Exercise18 point 5 Question 1 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 18 Indefinite Integrals Exercise18. 5 Question 1 Maths Textbook Solution.

Answers (1)

best_answer

Answer:  \frac{1}{6}(2 x+3)^{\frac{3}{2}}-\frac{1}{2}(2 x+3)^{\frac{1}{2}}+C

Hint: Use Integration by partial fraction

Given: \int \frac{x+1}{2x+3}dx

Solution:

= \int \frac{x+1}{2x+3}dx

\begin{aligned} &=\frac{1}{2} \int \frac{2 x+2}{\sqrt{2 x+3}} d x \\ &=\frac{1}{2} \int \frac{2 x+3-1}{\sqrt{2 x+3}} d x \\ &=\frac{1}{2} \int \frac{2 x+3}{\sqrt{2 x+3}} d x-\frac{1}{2} \int \frac{2 x+3}{\sqrt{2 x+3}} d x \\ &=\frac{1}{2} \int \sqrt{2 x+3} d x-\int(2 x+3)^{\frac{-1}{2}} \end{aligned}

 

=\frac{1}{2} \times \frac{1}{2} \int \frac{(2 x+3)^{\frac{1}{2}+1}}{\frac{1}{2}+1}-\frac{1}{2} \times \frac{1}{2} \int \frac{(2 x+3)^{\frac{-1}{2}+1}}{\frac{-1}{2}+1}                               \left[\therefore \int(a x+b)^{n} d x=\frac{\frac{1}{a}(a x+b)^{n+1}}{n+1}\right]

\begin{aligned} &=\frac{1}{2} \int \frac{(2 x+3)^{\frac{3}{2}}}{3}-\frac{1}{2} \times(2 x+3)^{\frac{1}{2}}+C \\ &=\frac{1}{6}(2 x+3)^{\frac{3}{2}}-\frac{1}{2}(2 x+3)^{\frac{1}{2}}+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 12 Supplementary Exam 2026: 'Chapter-wise weightage ignored,' allege students; seek grace marks
anam-khan

CBSE SARAS 7.0: Affiliation application deadline extended to September 30 for 2027-28 session
anam-khan

CBSE Class 12 supplementary exam 2026 on July 28; major subjects, timings, exam day guidelines

Latest Question