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Misc 41 - Class 12 - Integration - dx/ ex + e-x is equal

Misc 41 - Chapter 7 Class 12 Integrals - Part 2

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Misc 41 βˆ«β–’π‘‘π‘₯/(𝑒^π‘₯ + 𝑒^(βˆ’π‘₯) ) is equal to (A) tan^(βˆ’1) (𝑒^π‘₯ )+𝐢 (B) tan^(βˆ’1)⁑〖(𝑒^(βˆ’π‘₯) )+𝐢〗 (C) log⁑(𝑒^π‘₯βˆ’π‘’^(βˆ’π‘₯) )+𝐢 (D) log⁑(𝑒^π‘₯+𝑒^(βˆ’π‘₯) )+𝐢 βˆ«β–’π‘‘π‘₯/(𝑒^π‘₯ + 𝑒^(βˆ’π‘₯) ) = βˆ«β–’π‘‘π‘₯/(𝑒^π‘₯ + 1/𝑒^π‘₯ ) = ∫1β–’(𝑒^π‘₯ 𝑑π‘₯)/(𝑒^2π‘₯ + 1) Let 𝑒^π‘₯=𝑑 𝑑𝑑/𝑑π‘₯=𝑒^π‘₯ dt = 𝑒^π‘₯ 𝑑π‘₯ Substituting, = ∫1▒𝑑𝑑/(𝑑^2 +1) = γ€–π‘‘π‘Žπ‘›γ€—^(βˆ’1) (𝑑)+ C Putting value of t = 〖𝒕𝒂𝒏〗^(βˆ’πŸ) (𝒆^𝒙 )+ C Hence, answer is (A). (∫1▒〖𝑑π‘₯/(π‘₯^2 + 1)=γ€–π‘‘π‘Žπ‘›γ€—^(βˆ’1) π‘₯γ€— " " )

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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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.