Mathc initiation/a00a6

Sommaire

Calculons la primitive :

             
Calculer la primitive de 

       
   /               /            
  | sec(x)  dx =  | sec(x) *     (1)              dx     
  /               /                                         
    
                   /           sec(x) + tan(x) 
               =  | sec(x) * (-----------------)  dx                               
                  /            sec(x) + tan(x) 
                      
                                                             ___________________________________
                   /  sec(x)**2 + tan(x) * sec(x)            | u =    sec(x)     + tan(x)       |
               =  | (-----------------------------)  dx      |du = tan(x)*sec(x) + sec(x)**2 dx |                       
                  /      sec(x) + tan(x)                     |__________________________________|
                       
                       
   /               /            
  | sec(x)  dx =  | 1/u du     
  /               /                                         
                                   
               =   ln( |u| ) + c    
                                                           
               =   ln( |sec(x)+tan(x)| ) + c