I would like to look for it myself.
I would like to look for it by myself.
What is the difference between the two sentences above?
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Doing something "myself" indicated that I am the one doing it, in contrast with having someone else do it. "I know you said you couldn't find it, but I would like to look for it myself."
On the other hand, doing something "by myself" emphasizes that I am doing it alone, which can mean that no one is assisting me ("Please don't help. I would like to look for it by myself.") or that no other people are present ("Please leave the room. I would like to look for it by myself.").