Evaluate : ∫(3x-1)/(x+2)^2 dx ​

Question

Evaluate : \(\int\frac{3x-1}{(x+2)^2}dx\)

Answer 1

 Let \(\frac{3x-1}{(x+2)^2}\) = \(\frac{A}{(x+2)}+\)\(\frac{B}{(x+2)^2}\)

⇒ \(\frac{3x-1}{(x+2)^2}\) = \(\frac{A(x+2)+B}{(x+2)^2}\)

⇒ 3x - 1 = A(x + 2) + B 

⇒ 3x - 1 = Ax + (2A + B)

Equating the coefficient of x and constant term both side, we get

 A = 3,

2A + B = - 1

⇒ 2 x 3 + B = - 1

⇒ B = - 7