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Edited By Kuldeep Maurya | Updated on Jan 24, 2022 10:32 AM IST

The RD Sharma class 12 chapter 18 exercise 18.30 answers are trusted by the students on a large scale. Mathematics is a subject where many students lose marks due to lack of good practice. Therefore, it is essential for every student to own the RD Sharma Class 12 Exercise 18.30 reference book to perform well in their public exams. The 18th chapter of the class 12 mathematics syllabus consists of 31 exercises, ex 18.1 to ex 18.31. This counts to hundreds of questions that is present in this single chapter. RD Sharma solutions When it comes to ex 18.30, the difficulty of the questions would be higher as the exercises reach the end of the chapter.** **

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Chapter 18 - Indefinite Integrals - Ex-18.1

Indefinite Integrals exercise 18.30 question 1

To solve the given integration, we use partial fraction method

Let

Expressing the function in terms of partial fraction as following

On comparing the coefficient of x and constant terms we get

(1)

(2)

Now, subtract equation (2) from (1)

Putting the value of A in equation (1)

Now

Indefinite Integrals exercise 18.30 question 3

To solve the given integration, we use partial fraction method

Let

[Adding and subtracting 5 in numerator]

(1)

Let

Now express the function in terms of partial fraction

On comparing the coefficient we get

Equation (3)

Now

Putting the value of in equation (1)

Indefinite Integrals exercise 18.30 question 2

To solve the given integration, we use partial fraction method

Let

Now express the functions in terms of partial fraction

On comparing coefficient, we get

Now equation (2)

(4)

Equation (1)

(5)

Subtract equation (5) from equation (4)

Now equation (5)

Now

Indefinite Integrals exercise 18.30 question 4

To solve the given integration, we use partial fraction method

Let

[Adding and subtract in numerator]

Let

Comparing the corresponding coefficient

Adding equation (2) and (3)

Now equation (2)

Now

Now putting the value of in equation (1) and we get

Indefinite Integrals exercise 18.30 question 5

To solve the given integration, first we write the function in simple form and then apply the formula of integration

Indefinite Integrals exercise 18.30 question 6

To solve this integration, we use partial fraction method

Now

Indefinite Integrals exercise 18.30 question 7

To solve this integration, we use partial fraction method

Let

Indefinite Integrals exercise 18.30 question 8

To solve this integration, we use partial fraction method

Let

[Add and subtract 1]

…(applying the formula )

(1)

Where

Equation (1)

Indefinite Integrals exercise 18.30 question 9

To solve this integration, we use partial fraction method

Let

…(applying the formula )

Indefinite Integrals exercise 18.30 question 10

To solve this integration, we use partial fraction method

Let

[Add and subtract]

(1)

Where

Equation (1)

Indefinite Integrals exercise 18.30 question 11

To solve this integration, we use partial fraction method

Let

Let

Comparing coefficient

(1)

(2)

Subtract equation (1) from equation (2)

Equation (1)

Now

Indefinite Integrals exercise 18.30 question 12

To solve this integration, we use partial fraction method

Let

Let

(1)

Indefinite Integrals exercise 18.30 question 13

To solve this integration, we use partial fraction method

Let

Now

Comparing the coefficient

Indefinite Integrals exercise 18.30 question 14

To solve this integration, we use partial fraction method

Let

Comparing the coefficient

(1)

(2)

(3)

Subtract equation (3) from equation (1), we get

Equation (2)

Equation (1)

Now

Indefinite Integrals exercise 18.30 question 15

To solve this integration, we use partial fraction method

Indefinite Integrals exercise 18.30 question 16

To solve this integration, we use partial fraction method

Let

Comparing the coefficient

(1)

(2)

(3)

Equation (2)

Indefinite Integrals exercise 18.30 question 17

To solve this integration, we use partial fraction method

Let

Indefinite Integrals exercise 18.30 question 18

To solve this integration, we use partial fraction method

Let

Comparing the coefficient

(1)

(2)

(3)

(4)

Equation (3)

Equation (2)

Equation (4)

Now

Indefinite Integrals exercise 18.30 question 19

To solve this integration, we use partial fraction method

Let

Using the formulas,

Indefinite Integrals exercise 18.30 question 20

To solve this integration, we use partial fraction method

Let

Now

Indefinite Integrals exercise 18.30 question 21

To solve this integration, we use partial fraction method

Let

Indefinite Integrals exercise 18.30 question 22

To solve this integration, we use partial fraction method

Let

Comparing the coefficient

(1)

(2)

Multiply equation (2) by 2 and then

Subtract equation (1) from it

Equation (2)

Now

As

Indefinite Integrals exercise 18.30 question 23

To solve this integration, we use partial fraction method

Let

Let

(1)

At equation (1) becomes

At equation (1) becomes

Thus

As

Indefinite Integrals exercise 18.30 question 24

To solve this integration, we use partial fraction method

Let

(1)

At equation (1) becomes

At equation (1) becomes

At equation (1) becomes

At equation (1) becomes

Indefinite Integrals exercise 18.30 question 25

To solve this integration, we use partial fraction method

Let

Comparing the coefficient

Coefficient of

(2)

(3)

Coefficient of

(4)

Coefficient of

[From the equation (3)]

(5)

(6)

Constant term

(7)

Multiply the equation (4) by 4 and then subtract it from equation (7)

Equation (4)

Thus

Indefinite Integrals exercise 18.30 question 26

To solve this integration, we use partial fraction method

Let

Indefinite Integrals exercise 18.30 question 27

To solve this integration, we use partial fraction method

Let

Comparing the coefficient of and constant term

(1)

(2)

from equation (1)

(3)

from equation (1)

(4)

Subtract equation (3) from equation (4)

Equation (3)

Thus

Indefinite Integrals exercise 18.30 question 28

To solve this integration, we use partial fraction method

Let

Comparing the coefficient of and constant term

(1)

[From equation 1]

(2)

(3)

Multiply the equation (2) by 2 and subtract it from equation (3)

[From the equation (1)]

Equation (2)

Indefinite Integrals exercise 18.30 question 29

To solve this integration, we use partial fraction method

Let

Equating the similar terms, we get

(1)

(2)

(3)

Subtract equation (1) from equation (2) and we get

(4)

Multiply equation (1) by 6 and then adding equation (3)

(5)

Multiply equation (4) by 3 and then subtract it from equation (5)

Equation (4)

Equation (1)

Now

Thus

Indefinite Integrals exercise 18.30 question 30

Answer:Hint:

To solve this integration, we use partial fraction method

Given:

Explanation:

Let

Equating the similar terms

(1)

(2)

(3)

(4)

Adding equation (3) and (4)

Equation (3)

Indefinite Integrals Excercise 18.30 Question 31

To solve this integration, we use partial fraction method

Let

Equating similar terms

(1)

(2)

(3)

(4)

Adding equation (1) and (4)

Equation (2)

Equation (1)

Indefinite Integrals Excercise 18.30 Question 32

To solve this integration, we use partial fraction method

Let

Equating the similar terms

On solving we get

Thus

Indefinite Integrals Excercise 18.30 Question 33

To solve this integration, we use partial fraction method

Let

Equating similar terms

(1)

(2)

(3)

Equation (2)

Equation (1)

Indefinite Integrals Excercise 18.30 Question 34

To solve this integration, we use partial fraction method

Let

Equating the similar terms

(1)

(2)

Equation (1)

Indefinite Integrals Excercise 18.30 Question 35

To solve this integration, we use partial fraction method

Let

Equating the similar terms

(1)

(2)

Equation (2)

Equation (1)

Indefinite Integrals exercise 18.30 question 36

To solve this integration, we use partial fraction method

Let

Equating the similar terms

(1)

[From equation (1) and equation (2)]

Equation (2)

Equation (1)

Indefinite Integrals exercise 18.30 question 37

To solve this integration, we use partial fraction method

Let

Equating similar terms

(1)

(2)

Equation (1)

Equation (2)

Indefinite Integrals exercise 18.30 question 38

To solve this integration, we use partial fraction method

Let

Equating similar terms

(1)

(2)

Equation (1)

Equation (2)

Indefinite Integrals exercise 18.30 question 39

To solve this integration, we use partial fraction method

Let

Equating the similar terms

(1)

[From equation (1)]

(2)

[From equation (1)]

(3)

Equation (2)

(4)

[From equation (4) and (3)]

Equation (4)

And equation (1)

Indefinite Integrals exercise 18.30 question 40

To solve this integration, we use partial fraction method

Let

Equating the similar terms

(1)

(2)

[From equation (1) and (2)]

Equation (1)

Equation (2)

Indefinite Integrals exercise 18.30 question 41

To solve this integration, we use partial fraction method

Let

Equating the similar terms

(1)

(2)

[From the equation (1)]

[From the equation (1)]

(3)

[From the equation (2)]

Indefinite Integrals exercise 18.30 question 42

To solve this integration, we use partial fraction method

Let

Equating the similar term

(1)

[From equation (1)]

(2)

Equation (1)

(3)

(4)

Equation (3)

[From equation (4)]

Indefinite Integrals exercise 18.30 question 43

To solve this integration, we use partial fraction method

Let

(1)

Put in equation (1)

Put in equation (1)

Put in equation (1)

Thus

Indefinite Integrals exercise 18.30 question 44

To solve this integration, we use partial fraction method

Let

Equating similar terms

(1)

(2)

[From equation (1)]

Thus

Indefinite Integrals exercise 18.30 question 45

To solve this integration, we use partial fraction method

Let

…..(1)

For equation (1) becomes

For equation (1) becomes

For equation (1) becomes

[As]

Thus

Indefinite Integrals exercise 18.30 question 46

To solve this integration, we use partial fraction method

Let

[Multiply and divide by ]

Let

Now

Equating similar terms

Indefinite Integrals exercise 18.30 question 47

To solve this integration, we use partial fraction method

Let

[Multiply and divide by]

Let

Equating both side

Thus

Indefinite Integrals exercise 18.30 question 48

To solve this integration, we use partial fraction method

Let

Equating the similar terms

(1)

(2)

[From equation (1) and (2)]

Thus

Indefinite Integrals exercise 18.30 question 49

To solve this integration, we use partial fraction method

Let

Let

Now

(1)

Thus

Indefinite Integrals exercise 18.30 question 50

To solve this integration, we use partial fraction method

Let

Now let’s separate the fraction through the partial fraction

Put

Equating both side

Indefinite Integrals exercise 18.30 question 51

To solve this integration, we use partial fraction method

Let

Let

Put

Put

Indefinite Integrals exercise 18.30 question 52

To solve this integration, we use partial fraction method

Let

(1)

Put

Equation (1)

Put

Equation (1)

Indefinite Integrals exercise 18.30 question 53

To solve this integration, we use partial fraction method

Let

Let

(1)

Put

Equation (1)

Put

Equation (1)

Indefinite Integrals exercise 18.30 question 54

To solve this integration, we use partial fraction method

Let

[Multiply and divide by]

Let

As

Indefinite Integrals exercise 18.30 question 55

To solve this integration, we use partial fraction method

Let

Put

Put

Put

Put

Thus

Indefinite Integrals exercise 18.30 question 56

To solve this integration, we use partial fraction method

Let

Let

Put

Put

As

Indefinite Integrals exercise 18.30 question 57

To solve this integration, we use partial fraction method

Let

Equating both side

(1)

(2)

Indefinite Integrals exercise 18.30 question 58

To solve this integration, we use partial fraction method

Let

(i)

On comparing coefficient

Coefficient

(1)

Coefficient

(2)

Constant

(3)

(4)

Solving (2) and (4)

(1)

(3)

Multiply (1) by and subtract (3)

(i) Becomes

Indefinite Integrals exercise 18.30 question 59

To solve this integration, we use partial fraction method

Let

(1)

Indefinite Integrals exercise 18.30 question 60

To solve this integration, we use partial fraction method

Let

(1)

Put in (1)

Indefinite Integrals exercise 18.30 question 61

To solve this integration, we use partial fraction method

Let

Put

(1)

(2)

At

At

Put in (1) using (2)

Indefinite Integrals exercise 18.30 question 62

To solve this integration, we use partial fraction method

Let

Put

Differentiate w.r.t

(1)

Let

(2)

Put in (1) using (2)

Indefinite Integrals exercise 18.30 question 63

To solve this integration, we use partial fraction method

Let

(1)

Where

(i)

Comparing the coefficient

Coefficient

(2)

Coefficient

(3)

Coefficient

(4)

Constant

(5)

Multiply (3) by 4 and subtract it from (5)

(i) Becomes

Indefinite Integrals exercise 18.30 question 64

To solve this integration, we use partial fraction method

Let

Put

Let

Indefinite Integrals exercise 18.30 question 65

To solve this integration, we use partial fraction method

Let

Let,

Put

Put

Put

Indefinite Integrals exercise 18.30 question 66

To solve this integration, we use partial fraction method

Let

Let

Indefinite Integrals exercise 18.30 question 67

To solve this integration, we use partial fraction method

Indefinite Integrals exercise 18.30 question 68

To solve this integration, we use partial fraction method

Indefinite Integrals exercise 18.30 question 69

To solve this integration, we use partial fraction method

Let

(1)

Where

Indefinite Integrals exercise 18.30 question 70

To solve this integration, we use partial fraction method

Let

(1)

The topics in chapter 18, ex 30 includes assessing the integrals using mathematical replacements, sums regarding coordinating and its methods, joining the parts and so on. Other than the sums provided in the textbook, there are various other questions and solved answers in the RD Sharma Class 12 Solutions Chapter 18 Exercise 18.30 Indefinite Integrals reference book.

Benefits of picking the RD Sharma Mathematics solutions from the Career360 website:

Many professionals in the field of mathematics have contributed their work in creating the RD Sharma Class 12 Exercise 18.30 book from scratch. Therefore, there is no doubt regarding the accuracy of the answers.

Students can refer to these books while completing their homework and assignments. They need not wait for a teacher to clear their doubts.

It becomes easier for the students to recheck their homework and assignment before submission.

The sample question papers available with this material can be used to perform mock tests many times before the public exams.

The students gain clarity in the concepts that lets them face the exams with full confidence.

**RD Sharma Chapter-wise Solutions**

- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

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Download E-book1. What is the best reference guide that the class 12 students can depend on to complete their homework?

The best reference guide, Class 12 RD Sharma Chapter 18 Exercise 18.30 book helps the students anytime while doing the homework or assignments.

2. Where can the class 12 students find the RD Sharma Class 12 Solutions Chapter 18 Ex 18.30 at a low cost?

The best source website for the students to obtain the RD Sharma Class 12 Solutions Chapter 18 Ex 18.30 is the Career360 site.

3. How many solved sums for the 30th exercise for chapter 18 is available at the RD Sharma solutions book?

The RD Sharma Solutions Class 12 RD Sharma Chapter 18 Exercise 18.30 reference book consists of 70 solved sums.

4. What RD Sharma solution books help the Class 12 students achieve more marks?

The Class 12 students feel easy to attain more marks due to the many practice questions available in the RD Sharma Class 12th Exercise 18.30 book.

5. How can the students refer to the RD Sharma solution books offline?

The RD Sharma Class 12 Solutions Chapter 18 Exercise 18.30 reference book PDF can be downloaded from the Career360 website to be used offline.

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