# confused with u-subs problem

• Feb 22nd 2009, 05:49 AM
TYTY
confused with u-subs problem
integral of 1/(9 + 4x^2)

The book says u should be 2/3x. Can someone enlighten me on why this is? I am dumbfounded :(
• Feb 22nd 2009, 05:54 AM
mr fantastic
Quote:

Originally Posted by TYTY
integral of 1/(9 + 4x^2)

The book says u should be 2/3x. Can someone enlighten me on why this is? I am dumbfounded :(

Have you tried it ....?

Note that $\frac{1}{9 + 4x^2} = \frac{1}{9} \cdot \frac{1}{1 + \left(\frac{2x}{3}\right)^2}$.
• Feb 22nd 2009, 06:02 AM
TYTY
Quote:

Originally Posted by mr fantastic
Have you tried it ....?

Note that $\frac{1}{9 + 4x^2} = \frac{1}{9} \cdot \frac{1}{1 + \left(\frac{2x}{3}\right)^2}$.

please be patient with me here as I still don't understand this. (2x/3)^2 x 9 would have to equal 4x^2 again here right? but wouldn't it be (18x/3)^2 = 6x^2?

edit: I guess because of the square, you simplify using square root or something. The calculator agrees with your result but somehow it still goes over my head :(
• Feb 22nd 2009, 06:15 AM
mr fantastic
Quote:

Originally Posted by TYTY
please be patient with me here as I still don't understand this. (2x/3)^2 x 9 would have to equal 4x^2 again here right? but wouldn't it be (18x/3)^2 = 6x^2?

$9 \cdot \left( \frac{2x}{3} \right)^2 = 9 \cdot \frac{2x}{3} \cdot \frac{2x}{3} = 9 \cdot \frac{4x^2}{9} = 4x^2$.

If you're studying calculus it's expected you can do this. And do it easily.

I suggest you extensively revise basic algebra, index laws etc. if you hope to successfully tackle the sort of calculus questions you're going to get given n the coming days and weeks.
• Feb 22nd 2009, 06:20 AM
TYTY
Quote:

Originally Posted by mr fantastic
$9 \cdot \left( \frac{2x}{3} \right)^2 = 9 \cdot \frac{2x}{3} \cdot \frac{2x}{3} = 9 \cdot \frac{4x^2}{9} = 4x^2$.

If you're studying calculus it's expected you can do this. And do it easily.

I suggest you extensively revise basic algebra, index laws etc. if you hope to successfully tackle the sort of calculus questions you're going to get given n the coming days and weeks.

I imagine you're right about needing to review. I haven't taken any classes in 5 years now I find myself in this nightmare situation. Thank you for your explanation though - it did clear it up for me and now in retrospect it does seem kind of obvious.