Misc 14 - Integrate 1 / (x2 + 1) (x2 + 4) - Chapter 7 - Miscellaneous

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Misc 14 Integrate the function 1 2 + 1 2 + 4 Integrate 1 2 + 1 2 + 4 Let 2 = 1 2 + 1 2 + 4 = 1 + 4 + 1 Hence we can write 1 + 4 + 1 = + 4 + + 1 1 + 4 + 1 = + 1 + + 4 + 4 + 1 By canceling denominators 1 = A +1 +B +4 Putting = 1 1= A 1+1 +B 1+4 1= A 0+ B 3 1=3B B = 1 3 Similarly putting = 4 1= A 4+1 + B 4+4 1= A 3 + B 0 1= 3A A = 1 3 Therefore we can write 1 + 4 + 1 = 1 3 + 4 + 1 3 + 1 Putting = 2 1 2 + 4 2 + 1 = 1 3 2 + 4 + 1 3 2 + 1 = 1 3 2 + 4 + 1 3 2 + 1 Integrating w.r.t. 1 2 + 4 2 + 1 = 1 3 2 + 4 + 1 3 2 + 1 = 1 3 2 + 4 + 1 3 2 + 1 = 1 3 1 2 + 2 2 + 1 3 1 2 + 1 2 = 1 3 1 2 tan 1 2 + 1 3 1 1 tan 1 1 + = 1 6 tan 1 2 + 1 3 tan 1 + = +

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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.