Integrating exponential functions requires applying the inverse rules of derivatives of exponential functions. When integrating expressions with e^u, the integral is simply e^u/du. For integrals with a constant multiple, the constant is placed in the numerator and the denominator is adjusted accordingly. Definite integrals of exponential functions can be used to find areas bounded by the functions, which may require evaluating by hand to obtain exact answers.

1. 5.4b Exponential Functions: Integration Integrate natural exponential functions

2. Each of the rules for derivatives of exponential functions has a correlating integration rule. With e u you just need a matching du and you can put the chain back in the box!

3. Ex 7. p354 Integrating Exponential Functions Find Let u = 5x-1. Then du = 5dx. So I need a factor of 5 on the inside, and 1/5 on the outside. Back-substitute

4. Recall that you can multiply in constants, but cannot do that with missing variables that you might need. Ex 8 p. 354 Integrating Exponential Functions Find Rewrite to fit needs of du.

5. Ex 9 p. 355 Integrating Exponential Functions

6. Ex. 10 p. 355 Finding areas bounded by exponential functions Evaluate each definite integral. To get exact answers, you might need to evaluate by hand.

7. Ex 10 p. 355 Remember natural log rule where numerator is derivative of denominator!

8. Ex 10 p. 355 Use radian mode unless you know for sure angles are in degrees!

9. 5.4b p. 356/ 79, 85-109 odd 113-115, 120