# RD Sharma Class 12 Ex 19.5 Solutions Chapter 19 Indefinite Integrals

Here we provide RD Sharma Class 12 Ex 19.5 Solutions Chapter 19 Indefinite Integrals for English medium students, Which will very helpful for every student in their exams. Students can download the latest Sharma Class 12 Ex 19.5 Solutions Chapter 19 Indefinite Integrals book pdf download. Now you will get step-by-step solutions to each question.

## RD Sharma Class 12 Ex 19.5 Solutions Chapter 19 Indefinite Integrals

### Question 1.

Solution:

Given integral,

On Multiplying and dividing with 2, we get

⇒

⇒

⇒

⇒

By using the formula,

[where c is any arbitrary constant]

We get

⇒

⇒

⇒

⇒

### Question 2.

Solution:

Given integral,

Let x + 2 =t ⇒ x = t – 2

On differentiating on both sides,

dx = dt

On substituting it in given integral, we get

⇒

⇒

We know that,              [where c is any arbitrary constant]

⇒

⇒

Replacing x in terms of t

⇒

⇒

### Question 3.

Solution:

Given integral,

⇒

⇒

⇒

By using the formula,

[where c is any arbitrary constant]

We get

⇒

⇒

⇒

### Question 4.

Solution:

Given integral,

Let 3x + 5 = t

⇒ x = (t – 5)/3

On differentiating both sides,

dx = dt/3

On replacing the x terms with t,

⇒

⇒

⇒

By using the formula,

[where c is any arbitrary constant]

We get

⇒

⇒

On replacing t with x terms

⇒

⇒

⇒

### Question 5.

Solution:

Given integral,

On multiplying and dividing it with 3

⇒

⇒

⇒

⇒

By using the formula,

[where c is any arbitrary constant]

We get

⇒

⇒

⇒

⇒

⇒

### Question 6.

Solution:

Given integral,

Let 7x + 9 = t

⇒ x = (t – 9)/7

On differentiating both sides,

dx = dt/7

On replacing x terms with t

⇒

⇒

⇒

By using the formula,

[where c is any arbitrary constant]

⇒

⇒

On replacing t with x terms

⇒

⇒

### Question 7.

Solution:

Given integral,

⇒

⇒

By using the formula,

[where c is any arbitrary constant]

⇒

⇒

⇒

### Question 8.

Solution:

Given integral,

Let 1 + 3x = t

⇒ x = (t – 1)/3

On differentiating both sides, we get

dx = dt/3

On replacing x with t

⇒

⇒

⇒

By using the formula,

[where c is any arbitrary constant]

⇒

Now on replacing t in terms of x

⇒

⇒

⇒

### Question 9.

Solution:

Given integral,

Let 2x – 1 = t2

⇒ x = (t+ 1)/2

On differentiating on both sides,

dx = tdt

⇒

⇒

⇒

By using the formula,

[where c is any arbitrary constant]

⇒

On replacing t with x terms

⇒

⇒

⇒

⇒

### Question 10.

Solution:

Given integral,

On multiplying and dividing the given integral with

We know that (a + b)(a – b) = a– b2

⇒

⇒

⇒

⇒

By using the formula,

[where c is any arbitrary constant]

⇒

⇒

I think you got complete solutions for this chapter. If You have any queries regarding this chapter, please comment in the below section our subject teacher will answer you. We tried our best to give complete solutions so you got good marks in your exam.

If these solutions have helped you, you can also share rdsharmasolutions.in to your friends.