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in Indefinite Integral by (29.4k points)
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Evaluate the following integrals :

\(\int\frac{x^2+1}{x^2-5x+6}\)dx

1 Answer

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Best answer

Consider,

I = \(\int\frac{x^2+1}{x^2-5x+6}\)dx

⇒ 1 = A (x – 2) + B (x – 3) 

⇒ 1 = Ax – 2A + Bx – 3B 

⇒ 1 = (A + B) x – (2A + 3B) 

⇒ A + B = 0 and 2A + 3B = -1 

Solving the two equations, 

⇒ 2A + 2B = 0 

2A + 3B = -1 

- B = 1 

∴ B = - 1 and A = 1

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