2_Integration strategy

2_Integration strategy

1. STEP ONE

   • IF IT'S POSSIBLE, SIMPLIFY THE INTEGRAND
     • algebraic manipulation
     • TRIGONOMETRIC IDENTITIES

2. STEP TWO

   • SEARCH FOR AN OBVIOUS SITUATION
     • By using substituition

3. STEP THREE

   • is the integrand a rational expression integrand a polynomial divided by a polynomial?
     • USE PARTIAL FRACTION!
   • is the integrand a polynomial times a trigonometric function exponential or logarithm
     • USE INTEGRATION BY PARTS!
   • is the integrand a product of sin and cos, sec and tan or cot and csc?
     • USE INTEGRATION IDENTITIES!
   • integrand involve
     • • USE TRIGS SUBSTITUTION !
   • integrand have a quadratic in it ?
     • USE COMPLETING THE SQUARE !

4. STEP 4

   • MULTIPLE TECHNIQUES ??
     • ask yourselves if multiple techniques is possible or not
       • EXPERIENCE AND EXERCISES are important !

5. STEP 5

   • try again :)
     • if it still doesn't work, go back through the process and try again. try to use techniques that you haven't used.

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