Integrate the function in \frac{5x}{(x+1)({{x}^{2}}+9)}
Integrate the function in \frac{5x}{(x+1)({{x}^{2}}+9)}

Let I =  ……….(i)

Let  ……….(ii)

  

 

Comparing coefficients of  A + B = 0 ……….(iii)

Comparing coefficients of  B + C = 5 ……….(iv)

Comparing constants 9A + C = 0 ……….(v)

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

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

  From eq. (i),

I =