NCERT Solutions for Maths Class 12 Exercise 7.5

# NCERT Solutions for Maths Class 12 Exercise 7.5

Hello Students! In this post, you will find the complete NCERT Solutions for Maths Class 12 Exercise 7.5.

You can download the PDF of NCERT Books Maths Chapter 7 for your easy reference while studying NCERT Solutions for Maths Class 12 Exercise 7.5.

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NCERT Solutions for Maths Class 12 Exercise 7.1

NCERT Solutions for Maths Class 12 Exercise 7.2

NCERT Solutions for Maths Class 12 Exercise 7.3

NCERT Solutions for Maths Class 12 Exercise 7.4

NCERT Solutions for Maths Class 12 Exercise 7.6

NCERT Solutions for Maths Class 12 Exercise 7.7

NCERT Solutions for Maths Class 12 Exercise 7.8

NCERT Solutions for Maths Class 12 Exercise 7.9

NCERT Solutions for Maths Class 12 Exercise 7.10

## NCERT Solutions for Maths Class 12 Exercise 7.5

Integrate the rational function in Exercises 1 to 21.

Maths Class 12 Ex 7.5 Question 1.

Solution:

Let        …. (i)

x = A(x + 2) + B(x + 1)
x = Ax + 2A + Bx + B

Comparing coefficients of x on both sides, A + B = 1       …. (ii)

Comparing constants, 2A + B = 0       …. (iii)

Solving equations (ii) and (iii), we get, A = 1 and B = 2

Putting these values of A and B in equation (i), we get

Maths Class 12 Ex 7.5 Question 2.

Solution:

Maths Class 12 Ex 7.5 Question 3.

Solution:

Comparing coefficients of x2: A + B + C = 0      … (ii)

Comparing coefficients of x: –5A – 4B – 3C = 3

5A + 4B + 3C = –3                                        … (iii)

Comparing constants: 6A + 3B + 2C = –1         … (iv)

On solving eq. (i), (ii) and (iii), we get A = 1, B = –5, C = 4

Putting the values of A, B and C in equation (i), we get

Maths Class 12 Ex 7.5 Question 4.

Solution:

Maths Class 12 Ex 7.5 Question 5.

Solution:
Let
2x = A(x + 2) + B(x + 1)       … (i)
Putting x = –1, –2 in (i), we get A = –2, B = 4

= –2 log |x + 1| + 4 log |x + 2| + c

Maths Class 12 Ex 7.5 Question 6.

Solution:
Here, the given fraction is an improper fraction, therefore, we convert it into a proper fraction. Divide 1 – x² by x – 2x² by long division.

Maths Class 12 Ex 7.5 Question 7.

Solution:

Maths Class 12 Ex 7.5 Question 8.

Solution:

Maths Class 12 Ex 7.5 Question 9.

Solution:

Maths Class 12 Ex 7.5 Question 10.

Solution:

Maths Class 12 Ex 7.5 Question 11.

Solution:

Maths Class 12 Ex 7.5 Question 12.

Solution:

Maths Class 12 Ex 7.5 Question 13.

Solution:

2 = A(1 + x²) + (Bx + C) (1 – x)            … (i)
Putting x = 1 in (i), we get; A = 1
Also, 0 = A – B and 2 = A + C
B = A = 1 and C = 1

Maths Class 12 Ex 7.5 Question 14.

Solution:

3x – 1 = A(x + 2) + B                … (i)
On comparing coefficients, A = 3 and B = –7

Maths Class 12 Ex 7.5 Question 15.

Solution:

Maths Class 12 Ex 7.5 Question 16.

[Hint: multiply numerator and denominator by xn – 1 and put xn = t]
Solution:

Maths Class 12 Ex 7.5 Question 17.

[Hint: Put sin x = t]
Solution:

Maths Class 12 Ex 7.5 Question 18.

Solution:

Maths Class 12 Ex 7.5 Question 19.

Solution:

Maths Class 12 Ex 7.5 Question 20.

Solution:

Maths Class 12 Ex 7.5 Question 21.

[Hint: Put ex = t]

Solution:
Let ex = t ex dx = dt ⇒ dx = dt/t

Choose the correct answer in each of the following:

Maths Class 12 Ex 7.5 Question 22.

(D) log|(x – 1) (x – 2)| + C

Solution:

Maths Class 12 Ex 7.5 Question 23.

Solution:

Hence, the correct answer is option (A).