Mathc initiation/a00ak

Sommaire

Calculons la primitive :

             
Calculer la primitive de 

       
   /               /            
  | tanh(x)  dx =  |  sinh(x)/cosh(x) dx     
  /               /                                         
                        
                                       ________________________
                   /  sinh(x) dx       |     u =   cosh(x)    |
               =  |   -----            |     du =  sinh(x) dx |                       
                  /   cosh(x)          |______________________| 
                                       
                       
   /               /    1   du      
  | tanh(x)  dx =  |   -----     
  /               /     u                                    
                                                                 
                                   
               =   ln(   |u|     ) + c    
                                                        
               =   ln( |cosh(x)| ) + c