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 u will be the remaining factors. 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). OR

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

4. Integration by parts u = lnx dv= x 2 dx du = 1/x dx v = x 3 /3

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

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

7. 8.2 Trigonometric Integrals Powers of Sine and Cosine 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 and use for all other factors of cos. 3. If neither power is odd, use power reducing formulas:

8. Powers of sin and cos