A little help here please (study question)

[FlyingPig]

I'm using the Actex manual to study, and besides the amount of errors in the thing making me mad, I'm having trouble doing one of the practice problems. It's probably fairly obvious, but I can't figure out how they get the answer. I need to get the antiderivative for this, so I can solve for A, and then solve the problem, but I can't figure out how they get what they get. If somebody could show me what I'm missing I'd be very grateful.

Ae^t
------------------ = Population'(t)
(.02A + e^t)^2

Pop(0) = 6 billion
Pop(infinity) = 30 billion

[Travis]

let u = 0.02A + e^t
du = 0 + e^t dt

then ∫P'(t) dt = ∫A/u^2 du

I think you can take it from there

[FlyingPig]

See, I knew it was simple. That's really going to be my biggest stumbling block to passing the test. The tough stuff is easy, but I look right past the small stuff looking for the hard way... Thanks for answering.

[Travis]

no problem.

I don't know if you have access to this book, but the textbook I used in calculus was by James Stewart, and there's a section on how to attack integrals. If you can come by a copy of it, I'll look up the page numbers