Monkey Raptor

Saturday, October 11, 2014

Math: Let's Find the Solution of ∫ 2x∛(6x - 1) dx

I forgot to do it properly. And my brain crashed for a moment, a while ago. Therefore, I re-re-re-tinkered it on my scribble pad.
What do you know? It's not THAT complicated.

Anyway, this is a 12th grade Mathematics material.

We need patience.And cool stamina
2x∛(6x - 1) dx
It's using integration by parts

Let's Start

So then, we have bunch of variables, u — du — dv — v.
Let's use images then, as you can see below:
integral by parts variables

Plug them into the integration-by-parts formulation variables
integral by parts variables substitution

integral by parts solution #1


Probably we need another form of solution
Let's expand it once moar
integral by parts solution #2


Other method
We can also use tabular integration by parts method.
It's faster and much more organized, I suppose.
It's a great method for longer form which can be solved using integration by parts.
You can try using it by yourself, and see if the result will be the same as those two above.

How to decide whether using integral by parts or substitution?
I usually observe the difference of the exponents.


If like so:
example #1
Then use substitution.
But if like this:
example #2
Use the other method.
But then again, it depends on the problem. By doing problem sets repetitions, you'll have the "basic instinct".
Just like sport. But mostly with the conscious brain.

Tabular integration by parts at Wikipedia
Math: Let's Find the Solution of ∫ 2x∛(6x - 1) dx

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