164 PRACTICAL MATHEMATICS 



Then VX 2 + A 2 = AVl + sinh 2 = A cosh 



also X = A sinh 0, -^ = A cosh 0, or dX = A cosh dQ 



Then |Vx 2 + A 2 dX 

 = A 2 fcosh 2 0d0 

 = _f(l + cosh 20) dQ, since cosh 20 = 2 cosh 2 0-1 



= ^!{0 + sinh cosh 0} 



> 



or 



f 



or 



100 



The integral I VX 2 + A 2 dX, where X is a linear function of x, 

 can be solved by means of two standard forms. 



(2) 



X 2 + A 2 \ , X\/X 2 +A 2 ). 

 A 2 / 



(d) When the numerator of the fraction is of the second degree, 

 the fraction must be split up into three fractions. 



"7* I ^ / p 7 



(d) To integrate . 



Va; 2 + 4a? +12 



