Question

Evaluate the following integral : ∫1/(1+x+x²+x³)dx

\(\int\frac{1}{1+x+x^2+x^3}\)dx

Answer 1

I = ∫1/(1+x+x²+x³)

1 = (Ax + B)(x + 1) + C(x² + 1) 

Equating constants,

1 = B + C 

Equating coefficients of x,

0 = A + B 

Equating coefficients of x²,

0 = A + C 

Solving, we get