For integrals such as these: $$\int \frac{dx}{x^5(x+1)}, \int \frac{x^8dx}{x^3+x^2+2}, \int \frac{x^6dx}{x^4 + x^3 + 5x + 1}$$ Do easy methods/algorithms exist to evaluate them?
One method is to divide the numerator by the denominator. Another is to use partial fractions. Both of these are quite tedious and hard to do by hand. Are there other ways of doing these that I am missing?