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(a)  Let  (3x² – 4) / ( x² (3x – 2) ) = (ax + b) /x² + c/ (3x – 2)  = ( (c + 3a)x²+ (3b- 2a)x  -2b) /(x²(3x – 2) )

So  -2b =-4

b = 2

3b -2a = 0

a = 3

c+ 3a = 3

c = -6

(3x² – 4) / ( x² (3x – 2) ) = (3x + 1) /x² – 6/ (3x – 2) 

 

(b) ∫(3x² – 4) / ( x² (3x – 2) ) dx = ∫( (3x + 1) /x² – 6/ (3x – 2) ) dx

= 3 ln x – x-1 – 2 ln(3x-2) + c

 

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