Mathc initiation/a00a7

Sommaire

Calculons la primitive :

             
Calculer la primitive de 

       
   /               /            
  | csc(x)  dx =  | csc(x) *     (1)              dx     
  /               /                                         
    
                   /           csc(x) - cot(x) 
               =  | csc(x) * (-----------------)  dx                               
                  /            csc(x) - cot(x) 
                      
                                                             ____________________________________
                   /  csc(x)**2 - cot(x) * csc(x)            | u =     csc(x)     - cot(x)       |
               =  | (-----------------------------)  dx      |du = -cot(x)*csc(x) + csc(x)**2 dx |                       
                  /      csc(x) - cot(x)                     |___________________________________|
                       
                       
   /               /            
  | csc(x)  dx =  | 1/u du     
  /               /                                         
                                   
               =   ln( |u| ) + c    
                                                           
               =   ln( |csc(x)-cot(x)| ) + c