154 PRACTICAL MATHEMATICS 



integration must be a combination of the methods used in Case I. 

 and Case II. 



The fraction is now split up so that each part can be integrated 

 separately. 



dx C dx 



-) 2 +3 

 dX 



X 2 + A 2 



where X = x + 1 and A 2 = 3 



1 . i X 



= -r tan- 1 -r- 



A A 



1 x+ 1 



= 7= tan" 1 r= 

 A/3 V3 



4 f da; 2 



la: 2 + 2a; + 4 

 2) ^ log e (a; 2 + 2a; + 4) H ^= tan" 1 j=- 



1 , 2 . a? 2 - 4r + 4 4 , a? + 1 

 = -a; 2 + - log, + -7= tan- 1 r=- 



2 3 a; 2 + 2x + 4 ' Vs V9 



