Evaluate : ∫x+2/√(x^2+5x+6) dx

Question

Evaluate : \(\int \frac{x+2}{\sqrt{x^2+5x+6}}dx\)

Answer 1

Let I = \(\int \frac{x+2}{\sqrt{x^2+5x+6}}dx\)

Now, we can express as,

x + 2 = A(2x + 5) + B

⇒ x + 2 = 2Ax + (5A + B)

Equating coefficients both sides, we get

2A = 1,

5A + B = 2

⇒ A = \(\frac{1}{2},\) 

B = 2 - \(\frac{5}{2}\) = \(-\frac{1}{2}\)

∴  x + 2 = \(\frac{1}{2}\)(2x + 5)\(-\frac{1}{2}\)

Hence,