168 



Also 



dx 



PRACTICAL MATHEMATICS 



dx 



I2x - 10 



VBJ 



10 

 3 



22 



= 7llA7x^ whereX ^ + 2 



and A 2 =^ 



7= cosh" 1 V 

 A/3 A 



x+ 2 



cosh" 1 



1 A/3>+2) 



= r= cosh- 1 - 2-7= ' 



yi V22 



Or, expressing the result as a logarithmic function, 

 f dx I r rfX 



+ 12 - 10 



A/X 2 - A 2 



-L f X + VX 2 - A 2 \ 

 A/3 ge "|~ A J 



a; + 2 



-*J6 



2) 



- 10 



A/22 



Hence f 



J V 3 2 + 12a? - 10 



_4f (6x+l2}dx o r 

 3J A/3 2 + 12a? - 10 J 



8 . 

 = g V3x* 



8 /5-5 - TS - TTT 23 i / 

 or -V3 2 +12^-10 -- 7= log fl \ 



3 A/3 



+ I2x - 10 J V3Z 2 + I2x - 10 



_ M ,.. .A/8^+2) 



cosh* 



2) 



I2x - 10 



A/22 



