I am trying to find out the name of the song and artist that xfactor rachel sang in episode 1 :)

I think this is the song you mean. It's "With Every Heartbeat" by Robyn.

Maybe we could make it all right
We could make it better sometime

Maybe we could make it happen baby
We could keep trying
But things will never change

So I don't look back
Still I'm dying with every step I take
But I don't look back
Just a little, little bit better
Good enough to waste some time
Tell me would it make you happy baby

We could keep trying
But things will never change
So I don't look back
Still I'm dying with every step I take
But I don't look back

We could keep trying
But things will never change
So I don't look back
Still I'm dying with every step I take
But I don't look back

And it hurts with every heartbeat
And it hurts with every heartbeat
And it hurts with every heartbeat
It hurts with every heartbeat