Trick for Memorizing Trig Integrals

This video describes a method for helping students to memorize the Basic Trig Integrals.

For the Integral of Tan, - ln |cos u| + c and ln|sec u| + c are equivalent answers. To see the algebraic verification, follow this link:

#mathematics #calculus #trigintegrals

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For clarification, I did not create this mnemonic device for remembering trig integrals. Variations of this mnemonic device can be found all around the internet. For example, Tim Pettis presents a similar method in a Prezi Presentation, Mark Ryan presents a similar method in his book "Calculus Essentials for Dummies", MalignedAnus describes the method in a post on Reddit, and Vedant Mehta has created a YouTube video.

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[vdynamiic]

For 8 weeks, I struggled with these and you just made everything make sense in 7 minutes!!! Thank you so much, you are a lifesaver!!!!

[aryansingh]

2 years back saw ur same video. Just here to thank u as i still haven't forgot what u taught.

[TubeYous]

A good way to remember the integral of sinu = -cosu + c is just remember the list:
Sin
Cos
-Sin
-Cos
Then integration is up the list, and differentiation is down the list, and the list loops. Kinda hard to explain, but for example, the differential of sin is cos, and the differential of cos is -Sin. Then the differential of -Sin is -Cos, and the differential of that is Sin again, and so on. Then integration is the same, but reversed 'up' the list.

[KIKOMOON]

what a life saver!!! this was so clear and straight forward to help memorize a concept that makes no sense to most students. Once you understand the pattern, it literally takes 30 seconds. Whoever complained about the video length being 7min clearly don’t have the patience to understand and learn a tool that might help them pass

[laurencockerspaniel]

I was completely hopeless about memorizing these and you made it so easy! My teacher didn't so anything like this to help us, not even separating them into those helpful groups for us! Youre a lifesaver!!!!

[jonathoncliffbailey]

Calculus midterm tomorrow on integration by parts, trigonometric integrals, trigonometric substitution, integration of rational functions by partial functions, and improper integration. D: If it wasn't for videos like this then the master of procrastination would not be able to achieve such a feat. Great video. Instantly memorized! Now on to the hard stuff. :D

[SalAlhammadi]

The world need more teachers like you, your explanation are incredibly clear and straight to the point.



Thank you from the bottom of my heart <3

[Malaikas_creation]

It'a Malaika here from Pakistan....i saw many videos on integration but never solved my porblem..Thankyou so much ma'am u made it very easy to memorize me these formulas..amazing work..May God bless you with good health...plz pray for me..on 2nd March there is my Maths exam

[manishkota]

Who else is here the night before the test? Lets be real now

[Padthai_Shrimp]

Someone please many copies of these videos, they must be preserved!!!!

[patrickmayer]

Thank you for making sense of this madness! I'm glad people like you have found ways to make this easy to understand!

[connor]

The way I remember the anti-derivatives and derivatives of sin or cos is through a level system. If you imagine integration as going up a level and differentiation as going down a level then you just need to remember this:
-c
s
c
-s
where for derivatives -cosx derives to sinx, sinx derives to cosx, cosx derives to -sinx and then it loops to -sinx derives to -cosx and vice versa for integrals. This is what I was taught by my maths teacher and it helped me out a lot, it's second nature now.
When drawing the four letters I say in my head "C, S, C, S - Negatives at the ends"

[Rimedane]

A trick for sin to cos I like to say is "The Merry-Go-Round" because it goes sin -> -cos -> -sin -> cos -> sin. Because if you go far enough into Integration, it goes right back to where it started. Similar to e^x.

[Bukaloom]

Thank you so much, Cole. I'm taking Calculus II at CCNY and this helps tremendously.

[Mike-ksqu]

The only thing holding me back in calc 1 and 2 was this. Wow this helps so much. It's all fun and games on your exam until you see trig functions...

[andreyshor]

YOU ARE LITERALLY AMAZING! YOU SAVED ME ABOUT 3 HRS OF SLEEP! THANK YOU SO MUCH

[TamTran-uofz]

Bless your soul, for making a concept so understandable in 7 minutes. I am very grateful for your content.

[usthmember]

Amazing! "PSST" shows up in any page of my trig derivative calculations and now it will make integrating them a breeze too. You are truly amazing. Thanks so much for seeing this trend (or at least posting it)!

[redeem]

Thank you for this video! This was actually very helpful and I wish I would've found this information last semester because this is the easiest way I've seen to memorize these integrals.

[subby_tech]

Thank you very much! This video made it much easier to memorize the integrals of the trig functions!