Find f log x (1 + log x) ^{ 2 } dx
This question is similar to Ex 7.2, 35 - Chapter 7 Class 12 - Integrals
Last updated at Jan. 16, 2022 by
This question is similar to Ex 7.2, 35 - Chapter 7 Class 12 - Integrals
Transcript
Question 1 โ Choice 1 Find โซ1โใlogโก๐ฅ/(1 + logโก๐ฅ )^2 ๐๐ฅใ Let ๐=โซ1โใlogโก๐ฅ/(1 + logโก๐ฅ )^2 ๐๐ฅใ =โซ1โใ(๐๐๐โก๐ + ๐ โ ๐)/(1 + logโก๐ฅ )^2 ๐๐ฅใ =โซ1โใ((1 + logโก๐ฅ) โ 1)/(1 + logโก๐ฅ )^2 ๐๐ฅใ =โซ1โใ((1 + logโก๐ฅ) )/(1 + logโก๐ฅ )^2 ๐๐ฅใโโซ1โใ1/(1 + logโก๐ฅ )^2 ๐๐ฅใ =โซ1โใ(๐ )/((๐ + ๐๐๐โก๐ ) ) ๐ ๐ใโโซ1โใ๐/(๐ + ๐๐๐โก๐ )^๐ ๐ ๐ใ Solving โซ1โใ(๐ )/((๐ + ๐ฅ๐จ๐ โก๐ฑ ) ) ๐๐ฑใ Using Integration by parts โซ1โใ(๐ )/((๐ + ๐๐๐โก๐ ) ) ๐ ๐ใ = โซ1โใ(1 )/((1 + ๐๐๐โก๐ฅ ) ) ร 1 ๐๐ฅใ = 1/((1 + logโก๐ฅ)) โซ1โใ1 ๐๐ฅใโโซ1โ(๐ (๐/(๐ + ๐๐๐ ๐))/๐ ๐ โซ1โใ๐ ๐ ๐ใ) ๐ ๐ = 1/((1 + logโก๐ฅ))ร ๐ฅโโซ1โ((โ๐)/(๐ +๐๐๐ ๐)^๐ ร๐/๐ ร ๐) ๐ ๐ = ๐ฅ/((1 + logโก๐ฅ))+โซ1โ๐/(๐ + ๐๐๐ ๐)^๐ ๐ ๐ Thus I=โซ1โใ(1 )/((1 + ๐๐๐โก๐ฅ ) ) ๐๐ฅใโโซ1โใ1/(1 + ๐๐๐โก๐ฅ )^2 ๐๐ฅใ = ๐ฅ/((1 + logโก๐ฅ))+โซ1โ1/(1 + ๐๐๐ ๐ฅ)^2 ๐๐ฅโโซ1โใ1/(1 + ๐๐๐โก๐ฅ )^2 ๐๐ฅใ = ๐/((๐ + ๐๐๐โก๐))+๐ช
CBSE Class 12 Sample Paper for 2022 Boards (For Term 2)
Question 1 (Choice 2)
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8 (Choice 1)
Question 8 (Choice 2)
Question 9
Question 10 (Choice 1)
Question 10 (Choice 2)
Question 11
Question 12 (Choice 1)
Question 12 (Choice 2)
Question 13
Question 14 - Case Based
CBSE Class 12 Sample Paper for 2022 Boards (For Term 2)
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