c tT* f 



THE INTEGRALS j^= AND JVX 2 + A 2 



165 



Then 



x* + 5x - 7 



and each term can be integrated separately. 

 f Vz 2 + 4# + 12 dx = | V(x + 2) 2 + 8 dx 



J \/A 2 + X 2 dX where X = x + 2 

 and A 2 = 8 



A 2 r . 



where = 2 + 4r + 12 



| . aA where X = x + 2 and A 2 = 8 



JVX 2 +A 2 



i x 



smh- 1 -T- 



A 



, x + 2 

 = mnn- 1 



Then 



= sinh 

 - 7^ dx 



+ 



12 



f . 

 Va; 2 

 J 



, 

 + 4r + 12 dc + 



If (2^+4)^ n f 

 2J Va; 2 + 4a; + 12 J V : 



4, { sinh- 1 ^-^ + 

 2A/2 



. , . a;+ 2 

 - 21 smh- 1 7= 



2\/2 



12 



+ 4x + 12 



\ /-^ - - 



( H Vx 2 + 4c + 12 

 J 



