Given,
I = \(\int\frac{x^2}{x^2+7x+10}\)dx
⇒ 1 = A (x + 2) + B (x + 5)
⇒ 1 = Ax + 2A + Bx + 5B
⇒ 1 = (A + B) x + (2A + 5B)
⇒ A + B = 0 and 2A + 5B = 1
Solving the two equations,
⇒ 2A + 2B = 0
2A + 5B = 1
-3B = -1
∴ B = 1/3 and A = -1/3
Let u = x + 5 → dx = du