RD Sharma Solutions For Class 12 Maths Exercise 19.31 Chapter 19 Indefinite Integrals

Exercise 19.31 of Chapter 19, Indefinite Integrals consists of problems on integrals of the form \(\int \frac{x^{2}+1}{x^{4}+\lambda x^{2}+1}\ dx,\int \frac{x^{2}-1}{x^{4}+\lambda x^{2}+1}\ dx\). These problems are solved by BYJU’S experts in a descriptive way to speed up the exam preparation of students. RD Sharma Solutions for Class 12 provides detailed theory with illustrations, which makes learning easy for the students. These solutions will change every student’s approach towards Mathematics and help them learn all the concepts provided in the textbook. This exercise includes eleven questions.

Download the PDF of RD Sharma Solutions For Class 12 Chapter 19 – Indefinite Integrals Exercise 19.31

 

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Access answers to Maths RD Sharma Solutions For Class 12 Chapter 19 – Indefinite Integrals Exercise 19.31

Exercise 19.31 Page No: 19.190

Evaluate the following integrals:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 530

Solution:

The given equation can be written as,

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 531

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 532

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 533

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 534

Now, substituting t as x – 1/x and z as x + 1/x we have

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 535

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 536

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 537

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 538

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 540

We get,

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 541

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 542

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 543

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 544

Access other exercises of RD Sharma Solutions For Class 12 Chapter 19 – Indefinite Integrals

Exercise 19.1 Solutions

Exercise 19.2 Solutions

Exercise 19.3 Solutions

Exercise 19.4 Solutions

Exercise 19.5 Solutions

Exercise 19.6 Solutions

Exercise 19.7 Solutions

Exercise 19.8 Solutions

Exercise 19.9 Solutions

Exercise 19.10 Solutions

Exercise 19.11 Solutions

Exercise 19.12 Solutions

Exercise 19.13 Solutions

Exercise 19.14 Solutions

Exercise 19.15 Solutions

Exercise 19.16 Solutions

Exercise 19.17 Solutions

Exercise 19.18 Solutions

Exercise 19.19 Solutions

Exercise 19.20 Solutions

Exercise 19.21 Solutions

Exercise 19.22 Solutions

Exercise 19.23 Solutions

Exercise 19.24 Solutions

Exercise 19.25 Solutions

Exercise 19.26 Solutions

Exercise 19.27 Solutions

Exercise 19.28 Solutions

Exercise 19.29 Solutions

Exercise 19.30 Solutions

Exercise 19.32 Solutions

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