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Integrate the function in \frac{{{x}^{2}}+x+1}{{{(x+1)}^{2}}(x+2)}
CBSE | Class 12 | Integrals | Miscellaneous | NCERT
Integrate the function in \frac{{{x}^{2}}+x+1}{{{(x+1)}^{2}}(x+2)}

 Let I =  ……….(i)

Let  ……….(ii)

  

  

  

Comparing coefficients of  A + C = 1 ……….(iii)

Comparing coefficients of  3A + B + 2C = 1  ……….(iv)

Comparing constants 2A + 2B + C = 1  ……….(v)

On solving eq. (iii), (iv) and (v), we get  A = –2, B = 1, C = 3

Putting these values of A, B and C in eq. (ii),

  

= 

= 

= 

= 

i

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