What do you know? It's not

**THAT**complicated.

Anyway, this is a 12

^{th}grade Mathematics material.

*We need patience.*

_{And cool stamina}∫ 2x∛(6x - 1) dxIt'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:

Plug them into the integration-by-parts formulation variables

Continue...

Woo!

Probably we need another form of solution

Let's expand it once moar

WINNING!

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.

Anyway

How to decide whether usingintegral by partsorsubstitution?

I usually observe the difference of the exponents.

ExampleBut then again, it depends on the problem. By doing problem sets repetitions, you'll have the "basic instinct".

If like so:

Then usesubstitution.

But if like this:

Use the other method.

Just like sport. But mostly with the conscious brain.

Link

Tabular integration by parts at Wikipedia

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