Ex 7.2, 36 - Chapter 7 Class 12 Integrals (Term 2)
Last updated at Dec. 20, 2019 by
Last updated at Dec. 20, 2019 by
Transcript
Ex 7.2, 36 Integrate ((๐ฅ + 1) (๐ฅ + logโก๐ฅ )^2)/๐ฅ โซ1โใ" " ((๐ฅ + 1) (๐ฅ + logโก๐ฅ )^2)/๐ฅใ . ๐๐ฅ Let ๐ฅ+logโก๐ฅ= ๐ก Differentiating both sides ๐ค.๐.๐ก.๐ฅ 1+1/๐ฅ= ๐๐ก/๐๐ฅ (๐ฅ + 1)/๐ฅ= ๐๐ก/๐๐ฅ " " ๐๐ฅ = ((๐ฅ )/(๐ฅ + 1))๐๐ก Now, our function becomes โซ1โใ" " ((๐ฅ + 1) (๐ฅ + logโก๐ฅ )^2)/๐ฅใ . ๐๐ฅ Putting the value of ๐ฅโ๐๐๐โก๐ฅ=๐ก & ๐๐ฅ=((๐ฅ )/(๐ฅ + 1))๐๐ก = โซ1โใ" " ((๐ฅ + 1) (๐ก)^2)/๐ฅใ . (๐ฅ )/((๐ฅ + 1) ) . ๐๐ก = โซ1โใ" " ๐ก^2 ใ. ๐๐ก" " = ๐ก^(2 + 1)/(2 + 1) +๐ถ = ๐ก^3/3 +๐ถ = ๐/๐ (๐+๐๐๐โก๐ )^๐+๐ช (Using โซ1โ๐ฅ^๐ . ๐๐ฅ=๐ฅ^(๐+1)/(๐ +1)) (Using ๐ก=๐ฅ+๐๐๐โก๐ฅ)
Integration by substitution - lnx
Integration by substitution - lnx
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