How do you re-phrase pre-algebra problems in different ways to help understand the problem better?

You can use many different ways to describe algebra problems differently and find out shortcuts and keys to help learn pre-algebra easier.

How do you know when to integrate by parts versus trigonometric substitution versus trigonometric integration?

Integration by parts typically only include two integrating components multiplied together. Trigonometric substitution typically only includes integration that involves square roots in the denominator that have an exponential variable involved. Trigonometric integration involves using trigonometric identities to simplify the function you are integrating to a similar addition or subtraction integration.

How do you memorize the standard order of operations for learning Algebra?

Parenthesis first Exponents second MD (Multiplication and Division from left to right) AS (Addition and Subtraction from left to right) - PEMDAS!