Post 14 and 15

I was completely unaware that I had to do TWO blogs this week (didn't check edline, thanks to Ashley who now has me worrying about these), so here's all TWO of them...no wait..im only doing one:

One of them.

Substitution:

Okay, so I know the steps. They are extremely simple to understand; however, when I begin to actually do these steps I get thrown off by one thing: balancing. But anyway, here are the steps in my terms:

1. Identify your u (I identify this by looking inside the parentheses...and voila!)
2. Take the derivative of u to find your DU!!! (and don't forget the dx at the end)
3. Go back to original integration problem and substitute (ha! get it...substitution).
4. Then Integrate normal
5. Put all your u's back in to the original problem.

So for an example that I seriously get thrown of in (hint hint..if anyone would like to EXPLAIN this to me.....GREATLY APPRECIATED...just so you know...because I'm going to go insane).

Given:
S 6x(3x^2 + 4)^3 dx

Now I know my u is 3x^2 + 4.
My du is then 6x.

Subsitute the u and du

S du(u)^3

Now, in my notes I don't know what happens to this du..does it disappear?

Continuing the problem.

WHAT DO I DO WITH THE BALANCING THING!!! am I balancing the du or the u or WHAT???? I'm literally going insane...just to let you know...

I put a 1/6

so 1/6 [1/4(u)^4]

Final answer: 1/24(3x^2 + 4)^4

Is that right?? Can someone help me?

Also, as I'm sitting here to the packet what does the initial problems entail? I'm sitting here looking through my notebook for something that vaguely resembles these problems and am totally stumped. They are no where to be found....AMAZING! POOF!!! GONE!!!! pulled a flipping Houdini on me...apparently..


Now back to doing some other homework...by the way...I actually get some things in Calculus like basic Definite and indefinite...



OH!! I just remembered..what do you do when a number...say 7...is rasied to an exponent...say x^2...do I just substitute or what..and then how do i integrate that!??


HELP!!!!!!!!!!!!!!!!!!