Mathc initiation/a00a8

Sommaire

Calculons la primitive :

             
Calculer la primitive de 

       
   /               /            
  | tan(x)  dx =  |  sin(x)/cos(x) dx     
  /               /                                         
                        
                                       ___________________________
                   /  sin(x) dx        |     u =       cos(x)    |
               =  |   -----            |     du = (-1) sin(x) dx |                       
                  /   cos(x)           |(-1) du =      sin(x) dx | 
                                       |_________________________|
                       
   /               /   (-1)  du      
  | tan(x)  dx =  |   -----     
  /               /     u                                    
                                   
                                   
   /                    /  1       
  | tan(x)  dx =  (-1) |  ----- du     
  /                    /   u                                    
                                                        
                                   
               =  - ln(   |u|    ) + c    
                                               _______________________________________            
               =  - ln( |cos(x)| ) + c        | (-1) ln(a )         = ln( 1/a)        |
                                              | (-1) ln(|cos(x)|)   = ln( |1/cos(x)|) |
               =    ln( |sec|    ) + c        |                     = ln( |sec(x)|)   | 
                                              |_______________________________________|