this is my first post and I am a little concerned regarding notation, but I'll do my best to be as clear as possible in asking my question.
I am trying to find the recursive formula for evaluating the integral of In = [tangent x]^n
The book I am studying with gives as solution this:[1/(n -1 )]*[tangent x]^(n - 1) - I(n-2).
What I am getting, however, is something different. The way I am working is this:
I write [tangent x]^n as [tangent x]*[tangent x]^(n - 1). I proceed finding the derivative of the second multiplier and the integral of the first and proceed with the common steps of integration in parts method.
Now, since I get something different from what the book gives, I suspect two things. I either am rewriting the given function wrongly, and therefore I am getting a different answer, OR, the solution in the book is wrong.
I am not looking for someone to solve this problem for me, but I would appreciate it if someone could help me clarify if I am parting the function wrongly, or perhaps the solution given in the book is wrong?