A case of poor integration
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.
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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.