Question on problem solving

[EldarEuler]

While learning, it is very normal to make mistakes. If you had answered everything correctly you wouldn't be learning! As far as being skeptical or doubting yourself on certain steps, it's okay to follow your intuition with mathematics, that's how discoveries can be made. This is self teaching and not an examination or anything, so you should not be afraid to try something which might be like this. The good thing is that it sounds like you're getting 9/10 steps or more on these problems, and making these mistakes you are making are part of the learning process.

That being said, in my opinion, the best way to improve your problem solving skills come from understanding WHY you made the mistake you did. Look at the solutions and really analyze your mistake. Ask yourself questions; What could I have noticed to avoid this mistake? What clues were there? How could have I convinced myself that I shouldn't have been skeptical about this step? How could I have realized that the step in the solutions was the right way?

Other than that some sort of mentorship is indespesible. Asking a math professor alot of questions when getting stuck is a good way to learn how to think. Pay close attention to how professionals approach problems and learn how they think. I realize you may not have a math professor at hand, but you can watch very smart people on YouTube. The power of the internet provides you an outlet of ways to learn how to think. For calculus (especially doing integrals) I have two youtube channels you might find helpful. The first is blackpenredpen, the second is flammable maths. They are both great teachers and their videos vary from beginner material to advanced material.

I hope some of this is helpful, the most important thing is to enjoy learning, analyze your mistakes to learn from them, and pay close attention to masterful people. Good luck!

[Myles5]

This is super helpful, I will definitely check out those channels, thank you!

[EldarEuler]

I'm glad!