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Ex 7.5, 16 - Integrate 1 / x(xn + 1) - Class 12 NCERT - Integration by partial fraction - Type 1

Ex 7.5, 16 - Chapter 7 Class 12 Integrals - Part 2
Ex 7.5, 16 - Chapter 7 Class 12 Integrals - Part 3 Ex 7.5, 16 - Chapter 7 Class 12 Integrals - Part 4

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Transcript

Ex 7.5, 16 1 +1 [Hint: multiply numerator and denominator by xn 1 and put xn = t] We can write integrand as 1 + 1 = 1 + 1 1 1 = 1 + 1 = 1 + 1 Let t = Then = 1 Therefore 1 + 1 = 1 + 1 . 1 = 1 n + 1 We can write the integrand as 1 + 1 = + + 1 1 + 1 = + 1 + + 1 By cancelling denominator 1 = + 1 + Putting t = 0 in (1) 1 = 0+1 + 0 1 = = 1 Similarly putting t = 1 in (1) 1 = 1+1 + 1 1 = 0 1 = = 1 Therefore we can write 1 + 1 = 1 1 + 1 Thus, + 1 = 1 1 + 1 = log log +1 + C = log + 1 + Putting back t = 1 + 1 = + +

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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.