Ex 7.2, 36 - Integrate (x + 1) (x + log x)2 / x - Ex 7.2

Slide13.JPG

  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
Ask Download

Transcript

Ex 7.2, 36 ((๐‘ฅ + 1) (๐‘ฅ + logโก๐‘ฅ )^2)/๐‘ฅ Step 1: Let ๐‘ฅ+logโก๐‘ฅ= ๐‘ก Differentiating both sides ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ 1+1/๐‘ฅ= ๐‘‘๐‘ก/๐‘‘๐‘ฅ (๐‘ฅ + 1)/๐‘ฅ= ๐‘‘๐‘ก/๐‘‘๐‘ฅ " " ๐‘‘๐‘ฅ = ((๐‘ฅ )/(๐‘ฅ + 1))๐‘‘๐‘ก Step 2: Integrating the function โˆซ1โ–’ใ€–" " ((๐‘ฅ + 1) (๐‘ฅ + logโก๐‘ฅ )^2)/๐‘ฅใ€— . ๐‘‘๐‘ฅ Putting the value of ๐‘ฅโˆ’๐‘™๐‘œ๐‘”โก๐‘ฅ=๐‘ก & ๐‘‘๐‘ฅ=((๐‘ฅ )/(๐‘ฅ + 1))๐‘‘๐‘ก = โˆซ1โ–’ใ€–" " ((๐‘ฅ + 1) (๐‘ก)^2)/๐‘ฅใ€— . (๐‘ฅ )/((๐‘ฅ + 1) ) . ๐‘‘๐‘ก = โˆซ1โ–’ใ€–" " ๐‘ก^2 ใ€—. ๐‘‘๐‘ก" " = ๐‘ก^(2 + 1)/(2 + 1) +๐ถ = ๐‘ก^3/3 +๐ถ = ๐Ÿ/๐Ÿ‘ (๐’™+๐’๐’๐’ˆโก๐’™ )^๐Ÿ‘+๐‘ช

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.