Worksheet for Section 6.1–3Strategies for IntegrationMATH-UA 122.006: Calculus IISpring 2012Summary of Integration TechniquesStep 1.Simplify the integrand if possible, and use procedural rules to break down the integral (dis-tribute across sums, pull out constants, etc.)Step 2.Use the basic formulas like Formulas 1–20 in your table of integrals on reference page 6 (backpages). These are worth memorizing.Step 3.Make any substitution that will transform the integral into a simpler one.Step 4.Classify the integrand by “form”:I. Integration by parts.A. Polynomials are a good choice ofubecause they get simpler when differentiating.B. Inverse functions like ln, arcsin, arctan are also a good choice ofubecause they getsimpler when differentiating.C. Remember also that the product of an exponential and a sine or cosine can beintegrated by parts twice.II. Trigonometric forms:A.∫sinmxcosnx dx:•Ifmis odd, save sinx dxand letu= cosx.