Exercise 7.6
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NCERT Solutions class 12 Maths Integrals
Integrate the functions in Exercises 1 to 8.
1. 
Ans. 
= 
[Applying product rule]
= 
= 
= 
= 
2. 
Ans. 
= 
[Applying product rule]
= 
= 
= 
= 
3. 
Ans. 
= 
[Applying product rule]
= 
= 
= 
[Again applying product rule]
= 
= 
= 
= 
= 
4. 
Ans. 
= 
= 
[Applying product rule]
= 
= 
= 
= 
5. 
Ans. 
= 
= 
[Applying product rule]
= 
= 
= 
= 
6. 
Ans. 
= 
= 
[Applying product rule]
= 
= 
= 
= 
7. 
Ans. Let I = 
Putting 
I = 
= 
= 
= 
[Integrating by parts]
= 
= 
= 
= 
= 
8. 
Ans. Let I = 
= 
= 
= 
= 
= 
= 
= 
Integrate the functions in Exercises 9 to 15.
9. 
Ans. Let I = 
……….(i)
Putting 
From eq. (i),
I = 
= 
= 
[Applying product rule]
= 
= 
= 
= 
Putting 
and 
= 
= 
10. 
Ans. Putting
= 
= 
[Applying product rule]
= 
= 
[Again applying product rule]
= 
= 
= 
11. 
Ans. Let I = 
……….(i)
Putting
From eq. (i),
I = 
= 
= 
= 
[Applying product rule]
= 
= 
= 
= 
= 
12. 
Ans. 
= 
[Applying product rule]
= 
= 
= 
= 
13. 
Ans. Let I = 
= 
= 
= 
=
= 
14. 
Ans. 
= 
= 
= 
= 
= 
= 
= 
= 
15. 
Ans. 
= 
= 
[Applying product rule]
= 
= 
= 
= 
Integrate the functions in Exercises 16 to 22.
16. 
Ans. Let I = 
It is in the form of 
since here 
and 
I = 
17. 
Ans. Let I = 
= 
= 
I = 
It is in the form of since here 
and 
I = 
18. 
Ans. Let I = 
= 
= 
= 
= 
It is in the form of since here 
and 
= 
NCERT Solutions class 12 Maths Exercise 7.6
19. 
Ans. Let I = 
It is in the form of since here 
and 
I = 
= 
NCERT Solutions class 12 Maths Exercise 7.6
20. 
Ans. Let I = 
= 
= 
I = 
It is in the form of since here 
and 
= 
= 
.
I = 
NCERT Solutions class 12 Maths Exercise 7.6
21. 
Ans. Let I = 
= 
[Applying product rule]
I = 
I = 
[Again applying product rule]
I = 
= 
5I = 
I = 
NCERT Solutions class 12 Maths Exercise 7.6
22. 
Ans. Putting 
= 
= 
= 
= 
= 
[Applying product rule]
= 
= 
= 
= 
= 
NCERT Solutions class 12 Maths Exercise 7.6
Choose the correct answer in Exercise 23 and 24.
23. 
equals to
(A) 
(B) 
(C) 
(D) 
Ans. Let I =
= 
……….(i)
Putting 
From eq. (i), I = 
= 
=
Therefore, option (B) is correct.
24. 
equals:
(A) 
(B) 
(C) 
(D) 
Ans. Let I =
= 
It is in the form of since here 
and 
I = 
Therefore, option (B) is correct.