# Misc 24

Last updated at March 11, 2017 by Teachoo

Last updated at March 11, 2017 by Teachoo

Transcript

Misc 24 Integrate the function 𝑥2 + 1 log 𝑥2+ 1 − 2 log𝑥 𝑥4 𝑥2 + 1 log 𝑥2+ 1 −2 log𝑥 𝑥4𝑑𝑥 Taking 𝑥2common from 𝑥2+1 = (𝑥2) 12 1 + 1 𝑥2 12 log( 𝑥2+1) − log 𝑥2 𝑥4 𝑑𝑥 = 𝑥 1+ 1 𝑥2 12 log 𝑥2 + 1 𝑥2 𝑥4 𝑑𝑥 = 1+ 1 𝑥2 12 log 1 + 1 𝑥2 𝑥3 Let t = 1 + 1 𝑥2 𝑑𝑡𝑑𝑥= −2 𝑥3 −12𝑑𝑡= 𝑑𝑥 𝑥3 Substituting, = − 12 𝑡 12 log 𝑡 𝑑𝑡 Hence, − 12 𝑡 12 log𝑡 𝑑𝑡=− 12 log𝑡 𝑡 12 𝑑𝑡− 𝑑( log𝑡)𝑑𝑡 𝑡 12 𝑑𝑡 𝑑𝑡 = − 12 log𝑡 2 𝑡 323− 1𝑡× 23 𝑡 32 𝑑𝑡 = − 12 23 𝑡 32 log𝑡− 23 𝑡 12 𝑑𝑡 = − 12 23 𝑡 32 log𝑡− 23 2𝑡 323 = 29 𝑡 32− 13 𝑡 32 log𝑡 Putting value of t = 29 1+ 1 𝑥2 32− 13 1+ 1 𝑥2 32 log 1+ 1 𝑥2+ C = − 𝟏𝟑 𝟏+ 𝟏 𝒙𝟐 𝟑𝟐 𝐥𝐨𝐠 𝟏+ 𝟏 𝒙𝟐− 𝟐𝟑+ C

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Misc 24 Important You are here

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Integration Formula Sheet - Chapter 7 Class 12 Formulas Important

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.