Developers often suffer from impostor syndrome -- the feeling one doesn't deserve the accolades they receive, or have the skills or experience needed for the work they do (despite the quality of what they produce). But part of being a good programmer is accepting you can't know everything.
As developer Umer Mansoor writes, there's no point in using valuable brain space to remember something you can very easily look up. A novice coder might feel relying on Google or Stack Overflow is a bad thing when the opposite is true:
The resounding answer is YES, experienced (and good) programmers use Google… a lot. In fact, one might argue they use it more than the beginners ... Google is an essential part of their software development toolkit and they know when and how to use it.
Mansoor does however flag some caveats -- one shouldn't blindly copy and paste the snippets they find, rather, unless your needs are very basic, they should be used to validate your own solution:
[Good programmers] use Google to research possible solutions, carefully evaluating the results and consciously separating the wheat from the chaff ... Expert programmers are also paranoid, living in self-doubt and questioning their competence. Whenever their spidey senses start tingling, they know they may be going the wrong hole; So they rely on Google on validate their logic.
So don't let your pride or self-doubt get in the way of using search engines -- as Mansoor says, they're just another part of the toolbox.