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integration

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I am about to go to college and study engineering physics. I am studying calc based physics and Calculus BC, and some vector calculus (From the Stewart's textbook).

I think I am going to enroll in a introductory physics class that is more advanced than the usual intro for engineers and scientists this fall. My intro mechanics class will use Kleppner&Kolenkow, and my intro electricity will use math tools like Divergence, Grad, Curl to apply Maxwell's equations.

For those of you who went through that big jump between the rather easy high school physics and the more difficult college theoretical physics, what preparation did you wish you had done? I'm specifically interested in the math preparation, but physics advices are more than welcome.

I often hear that the big jump lies in the math. It's weird for me because setting up and solving integrals in calculus BC seems so easy, but when I have to use the same integrals for things like charge distributions, kinematics problems/momentum/acceleration, I often mess up the limits of integration, or forget a cosine component (I desperately working on Irodov's problems in physics right now, quite in vain actually), or I'm completely clueless on how to set the integrals with so many freaking confusing variables to deal with at the same time. Do you think that problem lies mainly in my lack of knowledge in vector calculus (and deep understanding of chain rule) and differential equations?

Do you have any suggestions for my preparation?

Thanks so much :D

PS: Keep in mind I have an intro textbooks for DiffE, linear algebra and vector calc that I am able to use.