Ex 7.5, 20 - Integrate 1/ x (x4 - 1) - Chapter 7 CBSE - Ex 7.5

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

Transcript

Ex 7.5, 20 1/( ( 4 1) ) Multiplying integrand by ^3/ ^3 1/( ( 4 1) ) = 1/( ( ^4 1) ) ^3/ ^3 = ^3/( ^4 ( ^4 1) ) Let t = ^4 Differentiating both sides . . . / = 4 ^3 /(4 ^3 ) = Substituting value of = ^4 & /(4 ^3 ) " " 1 ^3/( ^4 ( ^4 1) ) = 1 ^3/( ( 1) ) /(4 ^3 ) " " = 1/4 1 /( ( 1) ) We can write 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) 1 = = 1 Similarly putting t = 1 in (1) 1 = A(t 1)+Bt 1 = (1 1)+ 1 1 = 0+ 1 = = 1 Therefore 1/4 1 1/( ( 1) ) = 1 ( 1)/( ) + 1 1/( 1 ) = log | |+ log | 1|+ = log |( 1)/ |+ Putting t = ^4 1 1/( ( ^4 1) ) = / |( ^ )/ ^ |+

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