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dx / (x^2(9-4x^2)^(1/2)) using trig substituition, which I really don't understand.

Formula's that are useful:

The integral table

Integral 1/(u^2(a^2-u^2)^(1/2))=

-((a^2-u^2)^(1/2)) / (ua^2)

Work so far:

Figuratively banging my head against this problem for 4 days...

And so the answer I have is -((9-4x^2)^(1/2))/18x. Where-as my professor's answer is -((9-4x^2)^(1/2))/9x

So I am not even sure how to solve this correctly, nor am I sure of my answer...