derivative/ integral of exponential/log functions

I feel the #1 most useful integral (and derivative) is that of exponential function and the natural log function. Here is a

cheatsheet to be internalized.

for f (x) = e^x, f ' (x) = e^x

for f (x) = a^x, f ' (x) = ln(a) a^x

for f (x) = ln(x), f ' (x) = 1/x

for f (x) = log_a(x), then simpliy recognize f (x) = ln(x) / ln(a). The rest is really really simple.

Now the integrals

For f ' (x) = a^x, f (x) = a^x / ln(a)

For f ' (x) = ln(x), f (x) = x ln(x) – x See http://www.math.com/tables/integrals/more/ln.htm. Classic integration-by-parts

For f ' (x) = log_a(x), then simpliy recognize f ' (x) = ln(x) / ln(a). The rest is really really simple.