List of integrals of rational functions

The following is a list of <a href="/facts/Integral/V7lyV997">integrals</a> (<a href="/facts/Antiderivative/5qDsudIv">antiderivative</a> functions) of <a href="/facts/Rational_function/2nJGu0Ko">rational functions</a>. 
Any rational function can be integrated by <a href="/facts/Partial_fraction_decomposition/KLRmM3Hw">partial fraction decomposition</a> of the function into a sum of functions of the form:

a
            
              (
              x
              −
              b
              
                )
                
                  n
                
              
            
          
        
      
    
    {\displaystyle {\frac {a}{(x-b)^{n}}}}
  
, and 
  
    
      
        
          
            
              a
              x
              +
              b
            
            
              
                (
                
                  (
                  x
                  −
                  c
                  
                    )
                    
                      2
                    
                  
                  +
                  
                    d
                    
                      2
                    
                  
                
                )
              
              
                n
              
            
          
        
        .
      
    
    {\displaystyle {\frac {ax+b}{\left((x-c)^{2}+d^{2}\right)^{n}}}.}

which can then be integrated term by term.
For other types of functions, see <a href="/facts/Lists_of_integrals/FqW2wdwr">lists of integrals</a>.

List of integrals of rational functions open-in-new

List of integrals of rational functions