Situation Examples What to do All 6 trig functions Function can be integrated as is sec2x, csc2x, secxtanx, cscxcotx, Write the answer and be done with it! all polynomials, ex, ax, , Function and its derivative are U-substitution somewhere in the integrand Simple addition/subtraction Multiply top and bottom by the conjugate Quotient of polynomials where degree of numerator is degree of Long division ≥ denominator Quotient of polynomials where the Partial fractions denominator factors Products not yet covered, lnx, or all Integration by Parts inverse trig functions Exponentials * trig Wraparound IBP Polynomial Tabular method IBP • Involves a quadratic binomial Trig substitution
Situation Examples What to do Function can be integrated as is All 6 trig functions sec2x, csc2x, secxtanx, cscxcotx, all polynomials, ex, ax, , Write the answer and be done with it! Function and its derivative are somewhere in the integrand U-substitution Simple addition/subtraction Multiply top and bottom by the conjugate Quotient of polynomials where degree of numerator is ≥ degree of denominator Long division Quotient of polynomials where the denominator factors Partial fractions Products not yet covered, lnx, or all inverse trig functions Integration by Parts Exponentials * trig Wraparound IBP Polynomial • Tabular method IBP Involves a quadratic binomial Trig substitution
integration_flowchart.docx