Evaluating indefinite integral using integration by parts gives
Substracting from both sides we conclude
where is a constant.
Moreover, define as
it can be shown that
If we proceed to evaluate as follows:
we have (by (2-1))
Substracting from both sides (by (2-2)) we conclude
Unlike (1), (3) is true:
By the way,
See “Introducing Lady L” for details.
Exercise-1 Can you spot the fallacies?
Differentiating both sides, we have
Dividing both sides by (since ) yields