166 PRACTICAL MATHEMATICS 



= - 17 sinh- 



x + 2 1 . A . /-5 - 



= 17 sinh- 1 7= + r: fa + 4 ) V # 2 + 4# + 12 



2V2 2 



The result can also be expressed as 

 f(a? 2 + 5x 7) dx 

 J Vx 2 +4^+12 



= - 17 lo 



96. CW 777. (a) When the denominator of the fraction 



reduces to the form VX 2 A 2 , and in this case hyperbolic 

 functions must be used. 



(a) To integrate 



2 + 160 + 36 

 Now cc 2 + I6x + 36 = x 2 + IGx +64-28 



= (as + 8) 2 - 28 

 dx f dx 



Then 



J 



+ I6x + 36 JV>+8) 2 -28 



f. 



where X =x +8 and A 2 = 28 



JVX 2 - A 2 

 put X 2 = A 2 cosh 2 



then VX 2 - A 2 = AVcosh 2 0-1 = A sinh 



and X = A cosh 0, ~ = A sinh 0, or dX = A sinh 



at) 



I* JfV / / 



f rfx = p 



JVX 2 -A 2 J 



sinh 







A sinh 



= 



= cosh- 1 



f dx = ._ 



J ~ 



+ 



36 ~ 2 V7 



We also know that cosh = -r 



A 



