Integral Strategy

Integral Strategy

1. STEP 1

   • Simplify the integrand if possible

2. STEP 2

   • Look for an obvious situation
     • • By using substitution
         • • Thus, you can use substitution method instead of Partial fractions
             • NOTE

3. STEP 3

   • 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
   • Is the integrand involves
     • √(b^2 x^2+a^2 ),√(b^2 x^2-a^2 ),or √(a^2-b^2 x^2 ) ?
       • Use trigonometric substitution
   • Is the quadrant have a quadratic in it ?
     • Use completing the square

4. STEP 4

   • Do we use multiple techniques?
     • You need to ask yourselves either it is possible to use multiple techniques or not
       • This will be based on your EXPERIENCE

5. STEP 5

   • Try again
     • If you still didn't get the answer, then try the other technique that you didn't use yet

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