# Misc 32 - Chapter 7 Class 12 Integrals

Last updated at April 16, 2024 by Teachoo

Miscellaneous

Misc 1
Important

Misc 2 Important

Misc 3 Important

Misc 4

Misc 5 Important

Misc 6

Misc 7 Important

Misc 8 Important

Misc 9

Misc 10 Important

Misc 11

Misc 12

Misc 13

Misc 14 Important

Misc 15

Misc 16

Misc 17

Misc 18 Important

Misc 19 Important

Misc 20

Misc 21

Misc 22

Misc 23 Important

Misc 24 Important

Misc 25 Important

Misc 26 Important

Misc 27 Important

Misc 28

Misc 29 Important

Misc 30 Important

Misc 31 Important

Misc 32 You are here

Misc 33

Misc 34

Misc 35

Misc 36 Important

Misc 37

Misc 38 (MCQ) Important

Misc 39 (MCQ)

Misc 40 (MCQ)

Integration Formula Sheet - Chapter 41 Class 41 Formulas Important

Question 1 Important Deleted for CBSE Board 2024 Exams

Question 2 Important Deleted for CBSE Board 2024 Exams

Question 3 Important Deleted for CBSE Board 2024 Exams

Question 4 (MCQ) Important Deleted for CBSE Board 2024 Exams

Chapter 7 Class 12 Integrals

Serial order wise

Last updated at April 16, 2024 by Teachoo

Misc 32 Prove that โซ_1^3โใ๐๐ฅ/(๐ฅ^2 (๐ฅ + 1) )= 2/3ใ+logโกใ2/3ใ Solving L.H.S : โซ_1^3โ๐๐ฅ/(๐ฅ^2 (๐ฅ + 1) ) By partial fraction, 1/(๐ฅ^2 (๐ฅ + 1)) = A/๐ฅ+B/๐ฅ^2 +C/(๐ฅ + 1) 1/(๐ฅ^2 (๐ฅ + 1)) = ( A ๐ฅ (๐ฅ + 1) + B (๐ฅ + 1) + C๐ฅ^2)/(๐ฅ^2 (๐ฅ + 1)) โด 1 = Ax (x + 1) + B (x + 1) + C๐ฅ^2 Finding A,B,C โด 1/(๐ฅ^2 (๐ฅ + 1))= (โ1)/๐ฅ+1/๐ฅ^2 +1/(๐ฅ + 1) โซ1โ1/(๐ฅ^2 (๐ฅ + 1)) ๐๐ฅ=โซ1โ(โ1)/๐ฅ+1/๐ฅ^2 +1/(๐ฅ + 1) ๐๐ฅ = [โlog|๐ฅ|โ1/๐ฅ+log|๐ฅ+1|]_1^3 = [log|(๐ฅ + 1)/๐ฅ|โ1/๐ฅ]_1^3 Putting the limits = [log(4/3)โ1/3]โ[log(2)โ1] = "log" 4/3โ"log" 2 โ 1/3+1 = "log" (4/3ร1/2)โ1/3+1 = ๐๐๐(2/3)+2/3 = R.H.S Hence, proved.