1. I expect this is actually $\displaystyle \displaystyle \int{2x\sqrt{2x-3}\,dx} = \int{\frac{2x(\sqrt{2x-3})^2}{\sqrt{2x-3}}\,dx}$

$\displaystyle \displaystyle = \int{2x(\sqrt{2x-3})^2\left(\frac{1}{\sqrt{2x-3}}\right)\,dx}$.

Now make the substitution $\displaystyle \displaystyle u = \sqrt{2x-3}$.

2. Straight parts will work fine, though. Just in case a picture helps...

... where (key in spoiler) ...

Spoiler:

... is the product rule. Straight continuous lines differentiate downwards (integrate up) with respect to x. And,

... is lazy integration by parts, doing without u and v.

Spoiler:

Zooming in on the chain rule...

... where (key in spoiler) ...

Spoiler:

... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to the main variable (in this case x), and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

The general drift is...

_________________________________________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!

3. Originally Posted by Jeonsah
thanks for the help guys. This really helps out a lot.

Anyone know how to do the first problem?
Originally Posted by dwsmith
For 1,

$\displaystyle \displaystyle u=\sin^{-1}\left(\frac{x-1}{3}\right)$
Yes

4. man, you guys are good. thanks. Ill post up any other questions i have. I really enjoy this forum(its bookmarked) because people actually help here!

5. Hey guys got a question:

I have $\displaystyle f(x) = x^2$ and $\displaystyle f(x) = 9$

The problem is asking for the converse, inverse and contrapositive statments of those 2 functions. I am not familiar with this, can someone guide me what these mean?

6. Originally Posted by Jeonsah
Hey guys got a question:

I have $\displaystyle f(x) = x^2$ and $\displaystyle f(x) = 9$

The problem is asking for the converse, inverse and contrapositive statments of those 2 functions. I am not familiar with this, can someone guide me what these mean?
Start a new thread. There is no need for this thread to have a different question as you come across questions in the future.

7. alright thats cool. I just didnt wanna take up a bunch of space with a new thread. Thanks!

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