Integration of Exponential Functions: A Comprehensive Guide with Exercises, Slides of Differential and Integral Calculus

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INTEGRATION OF

EXPONENTIAL

FUNCTION

INTEGRATION OF EXPONENTIAL

FUNCTION

• (^) Define exponential functions;
• (^) Illustrate an exponential function;
• (^) Differentiate exponential function from

other

transcendental function function ;

• (^) provide correct solutions for problems

involving

exponential functions; and

OBJECTIVES:

Re call : d  e  e du u u     

u u e du d e Evaluate the integral of each side e du e C OR u u   

1. e dx

-5x 

EXAMPLE:

 

2. x e dx 4 3 x   dx e e
3. 2x- 3 6 x 2 x 2  

dx

e 2

x 

 dx

e

5. e

2 x 2 x

6. 3xe dx 3 1

• 3x 2  dx x 5

2 2 (^1 ) x 1 

1. 2 x dx

x 3 4 

EXAMPLE:



2. x 7 dx 3 4 3 x
3.  2 x 3 9 dx x 2 x 2  

EXERCISES: Evaluate the following integral.

3 x 1

e dx

 

e dx

1 0 2 x  1 2 x e dx x 

  3 2 3 1 2 x x e dx  e  sin e cos d    

 4 ( 2 x 1 )dx x 2 x 4 2 x x e dx e

   1 1 x 2 x dx 1 e e 4 1 x e dx x       d e sec tan sec f.