Wolfram|Alpha has a bug in its step-by-step presentation for integration by parts. (I use this often for my students.) E.g.:
WolframAlpha["integrate arctan(x)", {{"IndefiniteIntegral", 2}, "Content"}, PodStates -> {"IndefiniteIntegral__Step-by-step solution"}]
You can see the definitions:
The problem is: what is that "a
" doing there? (This is just a simple example, but more complex ones are hairier still.)
Note that the subsequent calculations are correct, and the a
is not there at all. This can be seen if one copies and pastes that equation, we observe that it is correct:
\[DifferentialD]g\[ThinSpace]== \[ThinSpace]\[DifferentialD]x
but for some reason a
is displayed instead.
I have submitted this to the Wolfram|Alpha folk, but as I use this quite a bit, I wonder whether someone has an idea for a workaround in the meantime.
Things I have tried: adding "dx
" to the initial command; changing the integration variable to y
or a
-- nada.
TYVM.
EDIT: I just noticed (and reported) that this bug is more prevalent, e.g., with integration by substitution:
WolframAlpha["integrate (4x-5)^9 from 1 to 3/2", {{"Input", 2}, "Content"}, PodStates -> {"Input__Step-by-step solution"}]
In this case, the bug disappears if the upper limit of integration is 2 (instead of 3/2), or just looking at the indefinite integral. (Help!)
Thank you again.