Integration Strategy

Integration Strategy

1. 4) Try again

   • Manipulate the integrand – usually works on trigonometric function
   • Try substitution again
   • Use several methods – can be 2 or 3 methods to solve an integral
     • example
       • completing square + inverse trigonometric
       • improper fraction + partial fraction
       • separating fractions + substitution

2. 2) Try simple Substitution

   • Could be faster than other technique
   • u = ax + b
     • du = x dx
   • Sometimes it's the easiest way

3. 3) Know the Integrand Type

   • Trigonometric functions – product of two trigo functions, can try substitution
     • sec^2xtanx
   • Quadratic funtions – can use completing square
     • X^2 + 2x + 6
   • Rational functions – may use partial fractions
     • (ax + b)^2 -> A/ax+b + B/(ax+b)^2
   • Product of polynomials and transcendental functions, can try integration by parts
     • ∫u dv = uv - ∫v du
   • Radicals – depends on the form, can use trigonometric substitution / rationalizing substitution
     • √(±x^2 ± a^2 )
     • √(n&g(x))

4. 1) Simplify Integrand

   • so that we can deal with the new form
   • Use basic trigonometric or algebraic identities
     • Reciprocal identities
     • Quotient Identities
     • Double Angle Formulas
     • Pythagorean Identities
     • Half Angle Formulas
     • Addition formulas