The problem is :- Integral of (1+x^4) / ( 1 + x^6) . dx I have reduced it to a form of Integral of 2.sqrt(tantheta) / ( 1 + tan^3 theta ) over dtheta where x^2 = tantheta. However I cannot reduce it further. How do I proceed ? In general, how do I proceed given a problem of the form of finding the integral of two polynomials when neither is a simple quadratic or factorized ?