Mathc initiation/a00al

Sommaire

Calculons la primitive :

             
Calculer la primitive de 

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