Misc 5 - Integrate 1 / x1/2 + x1/3 - Class 12 NCERT - Integration by substitution - x^n

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

Transcript

Misc 5 Integrate the function 1 1 2 + 1 3 1 1 2 + 1 3 Let x = 6 =6 5 dx = 6 5 dt Substituting value of x and dx = 6 5 ( 6 ) 1 2 + ( 6 ) 1 3 = 6 5 3 + 2 = 6 3 + 1 Adding and subtracting 1 in numerator = 6 3 + 1 1 + 1 = 6 3 + 1 + 1 1 + 1 = 6 + 1 ( 2 + 1 ) + 1 1 + 1 = 2 +1 1 1 + = 6 3 3 + 2 2 1+ + C = 2 3 +6 3 2 6 1+ + C Putting back value of t = 2 ( 1 6 ) 3 +6 ( 1 6 ) 3 ( 1 6 ) 2 6 1+ 1 6 + C = 2 1 2 +6 1 6 3 1 3 6 1+ 1 6 + C = 2 3 1 3 + 6 1 6 6 log (1+ 1 6 ) + 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.