<p>This is from a book with multiple choice questions for the "BC Exam," but obviously it might fall under AB, too...</p>
<p>∫[e^(2cot (x))]/[sin^2 (x)] dx =</p>
<p>(That's indefinite integral of e to the [2 cot (x)] all divided by [sin^2 (x)]...)</p>
<p>And if you guys want me to give you the answer choices, I can do that, too.</p>
<p>I was thinking I could just use a u-substitution, but that wasn't working out... at least not the way I was trying to do it.</p>
<p>Thanks!</p>
<p>geez...i really don't see that type of question being asked on the AP exam, AB or BC. they don't really test you on huge integrals like that (unless there's some little trick that makes it really really easy) on any section.</p>
<p>well, give the answer choices, just for the heck of it. maybe you could just find the derivatives of the answer choices and see if any of them match the integrand</p>
<p>Look at it this way: the derivative of cotx is -csc^2x</p>
<p>this is kind of a guess...is the answer .5e^(cot x) + C?</p>
<p>(yeah, there was a "trick" like i mentioned in the first reply...just took me a while to see it, lol)</p>
<p>-.5 e^(2cotx) + c </p>
<p>:p but I hoped you would be able to figure it out by that hint.</p>
<p>You, you got it.</p>
<p>I just realized that I was confusing the derivative of csc x with the derivative of cot x, so that probably contributed to my overall confusion...</p>
<p>Anyway, thanks! :D</p>
<p>haha, wow those are some dumb errors on my part, hopefully the question being multiple choice would make me realize those pointless mistakes. this is a bad sign; i'm taking the BC AP exam in a week and a half.</p>
<p>i actually to got my erroneous answer without your hint, but we were thinking the same thing.</p>
<p>on a side note, i didnt know you could type an integral thing on the computer.</p>
<p>Haha, neither did I until I saw someone else on here do it. I just copied and pasted it from Microsoft Word (under Insert > Symbol... towards the bottom).</p>
<p>I'm also taking the BC exam, and things like this I know how to do, I just need to practice a lot of multiple choice so that I avoid making stupid and time-wasting mistakes.</p>