FP3 integration standard forms could lead unwary pupils and teachers into a Pooh Trap. The following issue arises each year as the finer points of this course get sharpened.
When consulting the Edexcel formula sheet to find the integral,
two anti-derivatives are given,
Some might be tempted to infer that these functions are equal, this is the Pooh Trap, because whilst they both differentiate to they are not equal.
Play with exponential functions and quadratic equations give us the logarithmic form of which is also represented in formula books.
The two anti-derivatives differ by the constant .
In a definite integration, this constant is added and then taken away making no difference as to which anti-derivative the student uses. In a particular solution to a differential equation, the evaluation of the integral using boundary condition would lead to two different constant values.
The worse case is that a student takes the integration standard from and reads it as the logarithmic form of the inverse of . I have seen this happen.