To integrate a quotient like ∫(3x + x²)/(5x - 1) dx, one effective method is polynomial long division, which simplifies the integrand into a polynomial plus a proper rational expression. If unfamiliar with this technique, resources like Wikipedia can provide guidance on polynomial long division. Another approach involves a change of variable, such as letting t = 5x - 1, which allows for rewriting the integral in terms of t and dt, eliminating x and dx. Both methods facilitate the integration process by simplifying the expression. Understanding these techniques is essential for effectively integrating quotients.