integrate (x³+x+1)/(x⁴+x²+1) w.r.t x

Hi Suchita,

Split this to two integrals,

x³+x / x⁴ + x² + 1 and 1/(x⁴+x²+1). The second integral is a standard integral (integraded by standard method).

For the first integral, you have x(x²+1)/((x^2)²+x²+1}, make the substitution x²+1 = t, and xdx = dt/2

You will have t/{(t-1)² + t) dt = linear/Quad [again a standard integral, which one can integrate].

Hope that helps.

All the best,

Regards,

Ashwin (IIT Madras).