# NCERT Solutions for Exercise 7.6 Class 12 Maths Chapter 7 - Integrals

In NCERT solutions for Class 12 Maths chapter 7 exercise 7.6 functions like logarithmic, inverse trigonometric functions, exponential functions etc. are discussed in step by step manner. Solutions to exercise 7.6 Class 12 Maths are prepared in a holistic manner by subject matter experts. Hence NCERT solutions for Class 12 Maths chapter 7 exercise 7.6 provided below can be a good source. There is no need to refer to any other book for these topics as the content provided in the NCERT book is more than sufficient for the examination. Practicing from this exercise can help students score well in exams like JEE Main. The NCERT chapter Integrals also has the following exercise for practice.

Integrals Exercise 7.1

Integrals Exercise 7.2

Integrals Exercise 7.3

Integrals Exercise 7.4

Integrals Exercise 7.5

Integrals Exercise 7.7

Integrals Exercise 7.8

Integrals Exercise 7.9

Integrals Exercise 7.10

Integrals Exercise 7.11

Integrals Miscellaneous Exercise

** **

** ****Integrals ** **Class 12 ****Chapter 7** **Exercise: 7.6**

**Question:1 ** Integrate the functions

** Answer: **

Given function is

We will use integrate by parts method

Therefore, the answer is

### ** Question:2 ** Integrate the functions

### ** Answer: **

Given function is

We will use integration by parts method

Therefore, the answer is

### ** Question:3 ** Integrate the functions

### ** Answer: **

Given function is

We will use integration by parts method

Again use integration by parts in

Put this value in our equation

we will get,

Therefore, answer is

### ** Question:4 ** Integrate the functions

### ** Answer: **

Given function is

We will use integration by parts method

Therefore, the answer is

### ** Question:5 ** Integrate the functions

### ** Answer: **

Given function is

We will use integration by parts method

Therefore, the answer is

### ** Question:6 ** Integrate the functions

### ** Answer: **

Given function is

We will use integration by parts method

Therefore, the answer is

### ** Question:7 ** Integrate the functions

### ** Answer: **

Given function is

We will use integration by parts method

Now, we need to integrate

Put this value in our equation

Therefore, the answer is

### ** Question:8 ** Integrate the functions

### ** Answer: **

Given function is

We will use integration by parts method

Put this value in our equation

Therefore, the answer is

### ** Question:9 ** Integrate the functions

### ** Answer: **

Given function is

We will use integration by parts method

Now, we need to integrate

Put this value in our equation

Therefore, the answer is

### ** Question:10 ** Integrate the functions

### ** Answer: **

Given function is

we will use integration by parts method

Therefore, answer is

### ** Question:11 ** Integrate the functions

### ** Answer: **

Consider

So, we have then:

After taking as a first function and as second function and integrating by parts, we get

Or,

### ** Question:12 ** Integrate the functions

### ** Answer: **

Consider

So, we have then:

After taking as a first function and as second function and integrating by parts, we get

### ** Question:13 ** Integrate the functions

### ** Answer: **

Consider

So, we have then:

After taking as a first function and as second function and integrating by parts, we get

### ** Question:14 ** Integrate the functions

### ** Answer: **

Consider

So, we have then:

After taking as a first function and as second function and integrating by parts, we get

### ** Question:15 ** Integrate the functions

### ** Answer: **

Consider

So, we have then:

Let us take ** ....................(1) **

** Where, and **

** So, **

After taking as a first function and as second function and integrating by parts, we get

** ....................(2) **

After taking as a first function and as second function and integrating by parts, we get

** ................(3) **

** Now, using the two equations (2) and (3) in (1) we get, **

### ** Question:16 ** Integrate the functions

### ** Answer: **

Let suppose

we know that,

Thus, the solution of the given integral is given by

### ** Question:17 ** Integrate the functions

### ** Answer: **

Let suppose

by rearranging the equation, we get

let

It is known that

therefore the solution of the given integral is

### ** Question:18 ** Integrate the functions

### ** Answer: **

Let

substitute and

let

It is known that

Therefore the solution of the given integral is

### ** Question:19 ** Integrate the functions

### ** Answer: **

It is known that

let

Therefore the required solution of the given above integral is

### ** Question:20 ** Integrate the functions

### ** Answer: **

It is known that

So, By adjusting the given equation, we get

to let

Therefore the required solution of the given integral is

### ** Question:21 ** Integrate the functions

### ** Answer: **

Let

By using integrating by parts, we get

### ** Question:22 ** Integrate the functions

### ** Answer: **

** let **

Taking as a first function and as a second function, by using by parts method

### ** Question:23 ** Choose the correct answer

### ** Answer: **

the integration can be done ass follows

let

### ** Question:24 ** Choose the correct answer

### ** Answer: **

we know that,

from above integral

let

thus, the solution of the above integral is

**More About NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6**

The NCERT Class 12 Maths chapter Integrals is enough to have a command on this chapter. Exercise 7.6 Class 12 Maths provided here are step by step solutions and covers theoretical concepts also in the questions. NCERT solutions for Class 12 Maths chapter 7 exercise 7.6 is a one stop solution to score well in the exam.

**Also Read| **Integrals Class 12 Notes

**Benefits of NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6**

The Class 12th Maths chapter 7 exercise along with a reference book is sufficient for the good command.

Exercise 7.6 Class 12 Maths is on the similar line to that of exercise 7.5. So it will be easy to crack if one has already done exercise 7.5.

Class 12 Maths chapter 7 exercise 7.6 solutions provides good tricks to use in the exam for fastly solving the questions.

**Also see-**

NCERT Exemplar Solutions Class 12 Maths Chapter 7

NCERT Solutions for Class 12 Maths Chapter 7

**NCERT Solutions Subject Wise**

NCERT Solutions Class 12 Chemistry

NCERT Solutions for Class 12 Physics

NCERT Solutions for Class 12 Biology

NCERT Solutions for Class 12 Mathematics

**Subject Wise NCERT Exemplar Solutions**

NCERT Exemplar Class 12 Maths

NCERT Exemplar Class 12 Physics

NCERT Exemplar Class 12 Chemistry

NCERT Exemplar Class 12 Biology

Happy learning!!!