11 Strategies In Integration

11 Strategies In Integration

1. Basic Substitution

2. Completing The Square

3. Trigonometric Identities

   • cos2 x + sin2 x = 1
   • Addition Formula
     • cos( A + B ) = cos A cos B - sin A sin B
     • sin( A + B ) = sin A cos B + cos A sin B
   • Double-Angle Formula
     • cos 2x = cos2x -sin2x
     • sin2x = 2 sin x cos x
   • Half-Angle Formula
     • cos2x = ( 1+ cos2x) / 2
     • sin2x = (1 -cos2x) / 2

4. Improper Fractions

   • Use Long Division
   • Basic Substitution is not available

5. Separating Fractions

   • Basic substitution is not available

6. Multiplying By Form Of 1

   • When Trigonometric function cannot be integrate

7. Eliminating Square Roots

   • When Trigonometric Function Has Square Root
   • Need to sketch graph

8. Integration By Parts