Assuming that the Greek epsilon should read "e", the base of natural logarithms, the calculation is an attempt to find the length of an arc of the curve y = acosh(xa) - very important in civil engineering, as it is the shape taken by a uniform cable suspended freely from both ends.
Unfortunately, the bracket in line 2 has not been expanded correctly.
(i) exp(-xa) x exp(-xaexp(-2xa), which is the correct value of the third term in the third line, not exp(2xa) as shown.
(ii) exp(xa) x - exp(-xa-1, so the final term in the third line should be - 2 and not - 2e.
Mr Potter may be relieved to know that such errors are quite common even among A-level further maths students.
4 Downs Cote View
Editor's note: the image of the blackboard, reprinted above, came from a picture library, not Lawrence Potter's book. Thanks to both readers for pointing out the errors.