I teach Calculus and my students are often ill prepared.
Most Calculus problems, especially integration, are more than half doing Algebra, or Trigonometry.
You need to know
1/ How to Complete the Square of a quadratic
2/ How to do Polynomial Long Division
3/ Trig Identities, at least the Pythagoreans
4/ Trig manipulation
5/ Algebraic manipulation
6/ Polynomial rational function LCDs; adding polynomial fractions
7/ Good facility with Exponentials and Logarithms; and knowing they are Inverse functions
8/ Understanding of Inverse Trig Functions; Arccos x = thetaThen you will learn how to use judgement and intuition in making decisions.
But without the earlier Math you will be dead in the water even if you learn all the Calculus.
Go to purplemath dot com for the non trig topics
Cheers and good luck