Is this your integral?
Bare with me, I just registered so I have no idea how to type any signs ... difficult ones will be written out :o)sorry and thanks.
The problem: The integral from 1-e ((x^2+x+1)/x) dx
So far ... I got u= x^2+x+1 ; du= 2x+1 dx ; -1/2du= xdx <-- i'm not quite sure about this
Integral (1-e) ((x^2+x+1)/x) dx = -1/2 Integral (0-1) (u/du) ... And this is where I get stuck. Help please. Thnks
This might be a little above your level, maybe not.
So you have:
You can split off the 1.
so you pull the constant -e out.
This is where it starts to gets tricky. So the way I solved it was I used the fact that this is true:
So plugging in the x + 1/x you get:
So then you have:
Since the integral of a sum is the sum of the integral you can move that outside of the integral.
Then (x+1/x)^k is hard to work with but we have binomial theorem which states:
So you plug x and 1/x into binomial theorem and you have:
You move the sum out again:
the is a constant, it's also known as k choose i so you can pull it out.
So rewriting the term you get:
and lastly power rule:
but that's the solution, it's not . . . pretty though I'm not sure if there's a prettier way to write it.