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

Question

Evaluate the following integrals :

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

Answer 1

Given,
I = \(\int\frac{(1-x^2)}{x(1-2x)}\)dx

⇒ x – 2 = A (2x – 1) + Bx 

⇒ x – 2 = 2Ax – A + Bx 

⇒ x – 2 = (2A + B) x – A 

∴ A = 2 and 2A + B = 1 

∴ B = 1 – 4 = -3 

Thus,