Hello Students! In this post, you will find the complete 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.
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:
Solution:
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:
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.
Solution:
Solution:
Maths Class
12 Ex 7.5 Question 9.
Solution:
Solution:
Solution:
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.
⇒
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:
Solution:
Maths Class
12 Ex 7.5 Question 19.
Solution:
Solution:
[Hint: Put ex = t]
Solution:
Let ex =
t ⇒ ex dx = dt ⇒ dx = dt/t
Maths Class
12 Ex 7.5 Question 22.
(D) log|(x – 1) (x – 2)| + C
Solution:
Solution:
Related Links:
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