An important theorem in algebra says that every polynomial with real coefficients can be factored into first degree polynomials and irreducible quadratic polynomials with real coefficients. Furthermore, any rational function such that its denominator has the degree greater than its numerator, can be decomposed into partial fractions according to the rules stated above. The theorem says that decomposition into partial fractions is possible. Quite another matter is finding such decomposition for a given rational function. As you can quess, the first obstacle may be factoring the denominator, which often is a difficult task.
Maple can handle a variety of situations with simple commands.
Factor the denominator of w. Find the partial fraction decomposition. Find the indefinite integral of w. Compare the three. First let's define the expression w. Now we want to factor the denominator of w.