The derivation of the equation for the velocity of an object experiencing air resistance was long and tricky. I've prepared a PDF of it with notes about the steps. You can find it here.
https://drive.google.com/file/d/0B54jRZBDezIHSnB6UHFaWkRXMlE/view?usp=sharing
There is a minor mistake in the middle of the second page. Twice I write dt instead of u, in the denominator of the right hand side of the equation. This is in the section that I've labeled "now collect terms and integrate."
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