Starting: Derivatives are Easy, Integrals are Hard

Despite working over 20 years in Silicon Valley as a Software Engineer this is my first crack at a technical blog. I am not even fully sure what it is I will write about. If nothing else this will give me a break from my other hobby ... writing a blog about interpreting ancient religious texts.

What inspired me to start this was an incident last night going over my son's calculus homework.It was a relatively simple integral, as integrals go:

∫ x (x +2) dx / (x³ + 3x² -4) 

The answer is to sort of work backwards, since the derivative is easy, after setting the right value for u

1/3 ∫ (3x² +6x) dx / (x³ + 3x² -4)        where  u = x³ + 3x² -4  and therefore du /dx = 3x² +6x

this simplifies the equation to 1/3  ∫ du / u  =  1/3 ln | u | + c

then substituting back again we get the final answer    1/3 ln | x³ + 3x² -4 | + c

No big deal, but really all I did was simplify the equation to a form where I knew the derivative to the values in the integral. Derivatives are easy, integrals are hard.

I hope to use this blog to help simplify computing issues to simple doable ones. Just for fun here is a video on substitution for integral calculus