Integration by parts Puns

U d u

Examples? Do they have a name(s)?

Curseforge page:

https://www.curseforge.com/minecraft/modpacks/integration-by-parts

Discord server:

https://discord.gg/nQss77r

After an extremely long development cycle, Integration By Parts is fully released. With custom quest book themes, custom dungeons, and many other features, there is no shortage of things to do and sense of accomplishment for earning them. Want an expert pack with a long grind or creative item endgame? You might find what you are looking for here.

https://preview.redd.it/qvscn0jb78e41.png?width=2600&format=png&auto=webp&s=56181116b78408ac9dc0a172b366820efd2c93a9

I just cant seem to figure out whats wrong. The correct answer is 2ln(x+1) + 2(x+1)^-1. (Question is in image)

My working

Hello,

I have spent the past hour bashing my head against the screen trying to declutter this. So far I haven't been able to find a good solution and just make more of a mess. I'm not sure where to even start. The parentheses are killing me! ._.

Integration Problem

Thank you for your help.

So we had our lecture on integration by parts yesterday. Lecture is 1 hour and 15 minutes.

He scheduled an exam on Wednesday for us....for integration by parts.

Am I just a soft ass or does this seem like a rather quick turn around?

https://imgur.com/iZOxkel

So I’m asking what’s the General way to pick which expression or variable should be put as u and which should be put as dv when trying to solve a integral using intervention by parts.

If someone would like to answer how to decide between u and du for u-substitution that would also be amazing.

Thank you!!

Stuck here, am I on the right track? Been trying to get this whole concept down for a couple hours now where it requires multiple integrations.

Thanks in advance.

https://ibb.co/zmsW2r9

If anybody is struggling with U-substitution vs Integration by Parts, feel free to check out this video here. Over the past four years, these have been the major point of struggle among methods of integration.

https://youtu.be/v56CXyOc9j4

Also - if you have any feedback (things to keep / change) I'd love to hear your feedback. I teach in the US and almost all of our schools are out of session/learning remotely. My next video will likely be long division vs. partial fractions.

I have tried but I get to the second answer of Sqrt(4-x^2) x^4/4 - (1/4 int(x^5/srt(4-x^2).

I know there is a better way of doing it, but the professor wants it solved that way and I can't figure it out. :(

Edit: can*

So currently working through my variation by parameters work, and got stuck (needed an integration table, or so I thought). So far I got up to this but after that I got stuck. I realized that I’d have no other choice other than integrating it by parts. However, it’s been a bit since I’ve worked through it, and I can’t remember it exactly.

I know the equation is something like uv-S but I don’t remember after that.

Also feel free to correct me if I made a problem before this part (hoping I did so I don’t have to integrate this way).

I almost instantly recognized that this was the antiderivative of x^6*cos(x), but am unsure of how to show the work for it since work is required in order to receive credit for the problem. I am in Calc 1, so the class hasn't learned Integration by Parts yet and we aren't allowed to use anything that we haven't been taught in class (even if we teach ourselves outside of class). I am unsure of how to show my work for this problem without using Integration by Parts.

This is how I am showing my work currently, just showing that the derivative of x^6*cos(x) is 6x^5*cos(x) - x^6*sin(x). I don't think this will get me credit due to there being no actually antideriving in the work.

https://preview.redd.it/o36y9zikpcv31.jpg?width=4032&format=pjpg&auto=webp&s=860e25e940f932b038c6f88b554ab5f26627f7e1