How does one integrate a function where the numerator is a polynomial of degree $n$, and the denominator is a polynomial under root of degree $m$ $(m<n)$?
A random example being $$\int\frac{3x^4+2x^3+3x+9}{\sqrt{2x^2 +7x+5}}\mathrm{d}x$$
I cannot do long division as the denominator is under root, and neither can I use partial fractions for the same reason. Had the numerator been of the same degree or lower, it could have been expressed as $A(denominator) + B(\frac{d}{dx}denominator) + C$ - but that can't be used here. So, what should I do? (Change the coefficients of the function if you must. I want to get the basic idea.) Thanks.