# How much do you memorize to do general derivatives/integrals?

How much do you memorize to do general derivatives/integrals? While it is possible to do everything by going back to first principles, I imagine it gets exhausting to do so every time. So which derivatives/integrals do you memorize? Are the ones that I have attached to this post good enough to have memorized?

#### Attachments

• Untitled.png
4.4 KB · Views: 1,907

Stephen Tashi
How much do you memorize to do general derivatives/integrals?

You aren't describing a specific goal. Are you asking how much a student in second semester calculus should memorize? He would also need to know something about exponential functions.

arildno
Homework Helper
Gold Member
Dearly Missed
Well, I haven't thought of it, here's my typical rule
1. monomials of x (if power -1, logarithm)
1b). If in fractions, use fractional decomposition, logaritms for linear factors, arctan for irreducible squares.
2. Qaudratics under root sign: use trig subs,
3. Rational functions of polynomials in trig functions: Tan(pi/2)-substitutions
4. And exponentials.
5. Fiddling with product rule and substitution rule to get from 1 to 4, or give up.

You aren't describing a specific goal. Are you asking how much a student in second semester calculus should memorize? He would also need to know something about exponential functions.

I finished Calculus 1 and 2 and I'm currently taking a course in Differential Equations. I memorized the attachment above for Calculus 2 as advised by the textbook but I find that I have forgotten them over the break. It seems that I still need to have them memorized in order to do integration in Differential Equations but I want to get a general feel of how much I should re-memorize because I don't want to memorize more than I need to.

Well, I haven't thought of it, here's my typical rule
1. monomials of x (if power -1, logarithm)
1b). If in fractions, use fractional decomposition, logaritms for linear factors, arctan for irreducible squares.
2. Qaudratics under root sign: use trig subs,
3. Rational functions of polynomials in trig functions: Tan(pi/2)-substitutions
4. And exponentials.
5. Fiddling with product rule and substitution rule to get from 1 to 4, or give up.

I see that you have a general algorithm for integration, but do you memorize any derivatives or integrals? For example: you probably have memorized that the derivative of sinx is cosx or that that the derivative of lnx is 1/x.

mathwonk