Question

Evaluate the following integral : ∫ x/((x+1)(x²+1))dx

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

Answer 1

I =  ∫ x/((x+1)(x²+1))dx

x = A(x² + 1) + (Bx + C)(x + 1) 

Equating constants,

0 = A + C 

Equating coefficients of x,

1 = B + C 

Equating coefficients of x², 

0 = A + B 

Solving, we get