1. Chapter 7 Class 12 Integrals
  2. Serial order wise
  3. Ex 7.2
Check sibling questions

Ex 7.2, 19 - Chapter 7 Class 12 Integrals

Last updated at Dec. 16, 2024 by Teachoo

Transcript

Ex 7.2, 19 Integrate the function (𝑒2𝑥 − 1)/(𝑒2𝑥+ 1) Simplify the given function (𝑒^2𝑥 − 1)/(𝑒^2𝑥 + 1) Dividing numerator and denominator by ex, we obtain = (𝑒^2𝑥/𝑒^𝑥 " " −" " 𝟏/𝒆^𝒙 )/(𝑒^2𝑥/𝑒^𝑥 " " + " " 𝟏/𝒆^𝒙 ) = (𝑒^𝒙 − 𝒆^(−𝒙))/(𝑒^𝒙 + 𝒆^(−𝒙) ) Let 𝑒^𝑥 + 𝑒^(−𝑥)= 𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑒^𝑥+(−1) 𝑒^(−𝑥)= 𝑑𝑡/𝑑𝑥 𝑒^𝑥−𝑒^(−𝑥)= 𝑑𝑡/𝑑𝑥 𝑑𝑥=𝑑𝑡/(𝑒^𝑥 − 𝑒^(−𝑥) ) Now, Integrating the function ∫1▒〖" " (𝑒^2𝑥 − 1)/(𝑒^2𝑥 + 1) " " 〗. 𝑑𝑥 = ∫1▒〖" " (𝑒^𝑥 − 𝑒^(−𝑥))/(𝑒^𝑥 + 𝑒^(−𝑥) ) " " 〗. 𝑑𝑥 (Using (𝑒^2𝑥 − 1)/(𝑒^2𝑥 + 1)=(𝑒^𝑥 − 𝑒^(−𝑥))/(𝑒^𝑥 + 𝑒^(−𝑥) ) ) Putting 𝑒^𝑥 + 𝑒^(−𝑥)=𝑡 & 𝑑𝑥=𝑑𝑡/(𝑒^𝑥 − 𝑒^(−𝑥) ) =∫1▒〖" " (𝑒^𝑥 − 𝑒^(−𝑥))/𝑡 " " 〗. 𝑑𝑡/(𝑒^𝑥 − 𝑒^(−𝑥) ) " " =∫1▒〖" " 1/𝑡 " " 〗. 𝑑𝑡 =log⁡|𝑡|+𝐶 =log⁡〖 |𝑒^𝑥+𝑒^(−𝑥) |〗+𝐶 =𝒍𝒐𝒈⁡(𝒆^𝒙 + 𝒆^(−𝒙) )+𝑪 (Using 𝑡=𝑒^𝑥 + 𝑒^(−𝑥)) (As 𝑒^𝑥+𝑒^(−𝑥)>0 )
  1. Chapter 7 Class 12 Integrals
  2. Serial order wise

    3. Ex 7.2

    Ex 7.3 →
Ex 7.3 →
Chapter 7 Class 12 Integrals
Serial order wise

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo