# EXERCISE 7.5(Integration)

Integrate the rational functions in Exercises 1 to 21.(Ex 7.5 integration ncert maths solution class 12)

Question 1:

Solution:

Let putting in (i)

Again putting

Now, Integrating

Let

Question 2:

Solution:

Let

Let

Now

Integrating

Question 3:

Solution:

Let

Again Let

Again let

Putting the value of A, B and C in eq (i)

Integrating

Question 4:

Solution:

Let

Again Let

Again let

Putting the value of A, B and C in eq (i)

Integrating

Question 5:

Solution:

Let

Let

Putting in (i) and integrate

Question 6:

Solution:

Let

Let

Putting in eq (i) and integrate

Question 7:

Solution:

Let

Again let

Again let

Putting in (i) and integrate

Let

Question 8:

Solution:

Let

Let

Let

Putting the value of A, B and C in (i) and integrate

Question 9:

Solution: Since

Thus,

Now,

Let

Let

Let

Putting the value of A, B and C in (i) and integrate

Question 10:

Solution:

Thus,

Let

Let

Let

Putting the value of A, B and C and integrating

Question 11:

Solution:

Now,

Let

Let

Let

Putting the value of A,B and C in (i) and integrate

Question 12:

Solution:

Let

Let

Putting the value of A and B in (i) and integrate

Question 13:

Solution:

Let

Let

Let

Putting the value of A,B and C and integrate

Let

Now,

Question 14:

Solution:

Let

Let

Putting the value of A and B, and integrate

Question 15:

Solution:Let

Let

Let

Let

Puttinig in equation (i)

Integrating

Replacing

Question 16:

Solution: Let

Let

Differentiate w.r.t. x

Putting in (i)

Question 17:

Solution: Let

Let

Differentiate w.r.t. x

Let

Let

Putting in (i) and integrate

Question 18:

Solution: Let

Let

Let

Let

Putting the value of A and B and integrate

Question 19:

Solution: Let

Let

Using partial fraction

Let

Let

Putting in eq (i) and integrate

Question 20:

Solution: Let

Let

Adding and substracting t in numerator and denominator

Question 21:-

Solution: Let

Let

Putting in (i)

Let

Let

Thus,

Integrating

Choose the correct answer in each of the Exercises 22 and 23.

Question 22: equals

A.

B.

C.

D.

Solution: The correct Answer is B.

Let

Let

Let

Hence, the correct Answer is B.

Question 23: equals

A.

B.

C.

D.

Solution : The correct Answer is A.

Let

Let

Hence, the correct Answer is A.

Ex 7.4 integration ncert maths solution class 12