Question

Evaluate the following integral : ∫ 2x/(x³-1)dx

\(\int\frac{2x}{x^3-1}\) dx

Answer 1

I = ∫2x/(x³-1)dx

2x = A(x² + x + 1) + (Bx + C)(x – 1) 

= (A + B)x² + (A – B + C)x + (A – C) 

Equating constants, 

A – C = 0 

Equating coefficients of x,

2 = A – B + C 

Equating coefficients of x²,

0 = A + B 

On solving, 

We get,