Integration by parts

1. Integration by parts Product Rule:

2. Integration by parts Let dv be the most complicated part of the original integrand that fits a basic integration Rule (including dx). Then uwill be the remaining factors. OR Let u be a portion of the integrand whose derivative is a function simpler than u. Then dv will be the remaining factors (including dx).

3. Integration by parts u = x dv= exdx du = dx v = ex

4. Integration by parts u = lnx dv= x2dx du = 1/x dx v = x3 /3

5. Integration by parts v = x u = arcsin x dv= dx

6. Integration by parts u = x2 dv = sin x dx du = 2x dx v = -cos x u = 2xdv = cos x dx du = 2dx v = sin x

7. 8.2 Trigonometric Integrals 1. If n is odd, leave one sin u factor and use for all other factors of sin. 2. If m is odd, leave one cos u factor anduse for all other factors of cos. 3. If neither power is odd, use power reducing formulas: Powers of Sine and Cosine

8. Powers of sin and cos

9. Powers of sin and cos

10. Powers of sin and cos