# Thread: confused with u-subs problem

1. ## 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

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

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

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

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

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.

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

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.