I'm trying to find the integral . Here is what I did:
Let . Then so that , which is right.
My first question is, is there something wrong with the highlighted step? I have seen people raising questions about being treated as if they were numbers.
My second question is to do with when I tried to substitute for and got different results than the above:
Let . Then so that .
Getting two different results for the same integral is something I can't grasp at all.
There is nothing wrong with the substitution you have made in the first operation.
I hope you have learned trigonometry and you know that
so,
your first answer is
the second answer you have is
=
=
Note that is also a constant. So it gives you
So your answer by integration differ only by a constant