Board 8 > Today's nasty looking integral...

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FLOUR
02/17/25 4:03:50 PM
#1:


The integral of tan(x) / [sin(x) + cos(x) + 1]

The tricky part is first simplifying the dominator. After that it's relatively easy. All answers should be in terms of tan(x) and sec(x). Are you up to it?

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The alternate domination of one faction over another is itself a frightful despotism. - George Washington
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Uglyface2
02/17/25 4:21:44 PM
#2:


No, I'm not up to it. I've been watching a few math videos on YouTube, though, and I realize just how much I've forgotten.
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KingButz
02/17/25 4:30:21 PM
#3:


I got my degree so I wouldn't have to do homework anymore

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to me hero's is just bad person
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SeabassDebeste
02/17/25 4:43:22 PM
#4:


i tried a few substitutions with u = sin(x), u = cos(x), u = cos(x) * (sin(x) + cos(x) + 1), and u = (sin(x) + cos(x) + 1), but none of them really led me anywhere useful so i gave up. how would you do it?

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yet all azuarc of all sorts are more or less capricious and unreliable - they live in the varying outer weather, and they inhale its fickleness
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banananor
02/17/25 7:38:42 PM
#5:


Oh man, I hated integrations, at least after a certain level of complexity. Felt like a huge exercise in guess-and-check.

But maybe that just shows I didn't really understand what I was doing.

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You did indeed stab me in the back. However, you are only level one, whilst I am level 50. That means I should remain uninjured.
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SeabassDebeste
02/17/25 9:28:08 PM
#6:


actually i guess cos(x)+sin(x) is something like sqrt(2)cos(x-pi/4), so maybe that's a useful u sub

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yet all azuarc of all sorts are more or less capricious and unreliable - they live in the varying outer weather, and they inhale its fickleness
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FLOUR
02/17/25 10:04:23 PM
#7:


You guys really want a hint? Multiply the numerator and denominator each by [cos(x) + sin(x) -1].

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The alternate domination of one faction over another is itself a frightful despotism. - George Washington
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azuarc
02/18/25 12:07:15 PM
#8:


Ah, the good ol' multiply by the conjugate trick.

(I am just now seeing this thread, so I did not attempt it on my own first.)

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Only the exceptions can be exceptional.
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jcgamer107
02/18/25 12:07:43 PM
#9:


Uglyface2 posted...
No

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azuarc wasn't even home. he was playing Magic the Gathering at his buddy's store, which is extremely easy to verify
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NFUN
02/18/25 1:44:00 PM
#10:


I'm getting my degree so I have to do homework for classes instead

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No mule can match wits with me. Oh yes, many have tried, and almost all have failed!
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SeabassDebeste
02/18/25 2:10:41 PM
#11:


FLOUR posted...
You guys really want a hint? Multiply the numerator and denominator each by [cos(x) + sin(x) -1].

cool stuff, got it to work out after that, just need to look up integral of secant which i don't think i could've derived on my own

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yet all azuarc of all sorts are more or less capricious and unreliable - they live in the varying outer weather, and they inhale its fickleness
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