COMFY MATH THREAD /Integral bee/ edition

read the subject folks
Comfy math thread with a focus on cool integral problems. As usual though feel free to post anything you find interesting/are having trouble with. If you have any neat integrals or neat solutions to integrals (even if they're not your own) go ahead and post them.
I'm linking the MIT integration bee page because they have some pretty neat ones.
Also I learnt to into LaTeX so I'll try and use that from now on.
Pic related [2017 qualifier q 11] an easy little warm up that I hopefully haven't embarrassed myself with by screwing up.
Happy integrating and I'll post a few more as the thread gains traction.

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Math is anything but comfy asshole

Kill yourself you humongous faggot

Bro in the first integral in the bracket, use \Big( and \Big) instead

It's been 2 years since I took calc 2. What did you do to break up e^x*ln(x)dx into two like that? I wish my major was more math-intensive god damn it.

I was pretty good at integration in college, but it has been a while.
Please hit me up with an intermediate problem, OP.

if you feel that way then why bother posting guys?
I'll take the free >(you)s anyway though
didn't think it was needed but I am familiar with \big( \bigg( etc...
it's integration by parts, a proof of it will be my next post actually
difficulty of integrals is often subjective, sometimes you just see things, try this one though

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What level problems are these? They seem extremely basic.

yeah they're integral bee problems so the idea is that they ought to be solvable in a minute or two.
If you want we can do the Gaussian or the Dirichlet or some other cool integrals, or integrals that resolve to those big name integrals. Remember that it's a comfy math thread, so we want cool tricks rather than laborious algebra or transformations.

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here's a harder one for you

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Just go to /sci/ for math generals.
Of course you will get laughed at for making a thread about integrals which is baby tier math.

sorry mang, cant solve it. tried a couple of the first MIT integration bee exercises and solved most of them, but now i feel like a fuckin brainlet. ;_;

>19 year olds taking Analysis 1 decide to enlighten everyone with their supreme knowledge of basic integration

>calculus
>antiderivatives
>comfy
Only the 3 branches of abstract mathematics are comfy, applied maths is for normies

>enlighten everyone
was clearly never the purpose of this

I understand it's baby tier, that's why I picked integral bee questions and labelled it a comfy math thread. If I wanted to watch brainlets beat themselves off because they think they're geniuses because they understand (tenuously) that the sum of all natural numbers isn't -1/12 I'd have posted it on /sci/
well if you're out of practice sometimes you're just not going to see the necessary tricks. Also my solution for this one uses a trig identity so if you've forgotten those you might have trouble. Definitely begin by rewriting csc(x)sec(x) as 1/sin(x)cosx).

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I had an idea to partially integrate (cos2x * tan2x)^-1 but it really seems like a dead end...

it's really not you basically solved it
cos2x*tan2x is just sin 2x
although there should have been a 2 moved out to the front of the integral iirc
it ends up becoming the integral of cosec2x, which is just a standardised integral but can be tricky if you haven't seen it
I'll do a full write up of this integral and the other one I posted

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Should the average Wizard bother to learn math?
Will it help me improve my quality of life?

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sorry this took so long anons
I had to prepare some things for an Easter feast tonight. Any other orthodox anons in the thread?
pic is solution to this problem
It'll be a self worth thing most likely. Though if you like puzzles in general you'll probably just enjoy math for its own sake.

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This shit would look far less complicated if you just changed the infinity to a real number. You're a fucking faggot if you think you're the next einstein for posting basic integration onto a congolese diamond mining forum.

Dude do you actually find calculus at all exciting?
Have you not done a paper in algebra, analysis or discrete mathematics?

but the infinite series doesn't converge nicely without the infinity. Sure there's a formula for it anyway but it's a less pretty solution. I didn't make this problem either, I found it on youtube.
I literally never even claimed to be good at math, I just want to discuss it with other interested robots, who said it had to be a pissing contest.

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Really? I thought about inegration by parts but that result looked wrong to me. I'll just do it out desu.

I haven't, I'm just a first year math student. Yes I'm essentially a beginner and enjoy integral problems, sue me.

o shit nigga know don't do it out by parts, I assumed you'd gotten it to cosec2x, which is a standard integral. I don't think IBP would work but it might I suppose.
my solution's coming soon.

3rd year here, still a pleb but it gets a whole lot more interesting than calculus if you stick with it

I look forward to it
I've dabbled in some light analysis, number theory and topology but nothing too formal as of yet.
Got to go guys, safeguard the thread for me.