Evaluate the following integrals : ∫ (x^2+x+1)/(x^2-x)dx ​

Question

Evaluate the following integrals :

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

Answer 1

Given,

I = \(\int\frac{x^2+x+1}{x^2-x}\)dx

Expressing the integral

⇒ 2x + 1 = Ax + B(x – 1) 

⇒ 2x + 1 = Ax + Bx – B 

⇒ 2x + 1 = (A + B)x – B 

∴ B = -1 and A + B = 2 

∴ A = 2 + 1 = 3 

Thus,