Misc 24 - Integrate root x2+1 [ log (x2 + 1) - 2 log x / x4 - Miscellaneous

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Misc 24 Integrate the function 2 + 1 log 2 + 1 2 log 4 2 + 1 log 2 + 1 2 log 4 Taking 2 common from 2 +1 = ( 2 ) 1 2 1 + 1 2 1 2 log ( 2 +1) log 2 4 = 1+ 1 2 1 2 log 2 + 1 2 4 = 1+ 1 2 1 2 log 1 + 1 2 3 Let t = 1 + 1 2 = 2 3 1 2 = 3 Substituting, = 1 2 1 2 log Hence, 1 2 1 2 log = 1 2 log 1 2 ( log ) 1 2 = 1 2 log 2 3 2 3 1 2 3 3 2 = 1 2 2 3 3 2 log 2 3 1 2 = 1 2 2 3 3 2 log 2 3 2 3 2 3 = 2 9 3 2 1 3 3 2 log Putting value of t = 2 9 1+ 1 2 3 2 1 3 1+ 1 2 3 2 log 1+ 1 2 + C = + + + C

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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.