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Example where we do substitution twice to get the integral into a reasonable form
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Sal: WHEN WILL THIS MFING CROW STFU?!
Crow: NEVERMORE!
Put the e term in the numerator, notice the cos5x obviously being a derivative of sin5x (ignore constants), take a derivative of the exponential term and adjust by multiplying by a constant, and done
That's one u sub two many.. Quoth the raven… Sol means solution to us bird brains…. Thanks again for helping, God bless 🙏
Omg it took me like 3 hours to solve a problem like this thank you
Shout out to that crow though
Nice but it could be easier if just take it as exp(-u)= exp(-1.u)=exp(a.u)
Where a=-1
6:26 “… really hold yourself, feel too bad if you didn't see that insight …” 😂😂😂 on point Sal. You r really a nice human being over all i think.
couldn't the answer just be 1/5 ln(e^sin(5x)) ?????
Edgar Allen Poe is a Math teacher. Amazing
Couldn't you just do power rule of e^-u after the first integral to get the e^u * u' which would result in your -e^u? (Times the 1/5 in front of course)
Sal thank u very much
who thought of hey arthur when he said D-W hahaha
This helped me so much! I just transferred from a community college into a four year school, and I'm currently taking cal 2 at my new school. However, I did not learn anything from my cal 1 class, so been suffering in my cal 2 class. I watched 4 of your videos now, and they are great. I will keep use your videos to study, and thank you for your videos.
really good crow commentary on this one
That crow is taking Calc as well bruh
what if i simply just sub u=sin(5x)
Guess you can call it Double-U substitution, ayyyyeeee
but how do the limits change if you do 2 substitutions??
wen hes doing the simpler method he says the du/dx of -sin(5x) = -5 cos(5x), correct me if im wrong but isnt the d/dx sin(5x)= -5 cos(5x). wouldnt the – infront of the sin affect the – in the -5cos5x ? lol sorry if this doesnt make sense
Dang Crow haha
I've never heard such a smooth phrase, than 'I hope you dont't hear that crow outside, he's getting quite obnoxious.'
So, Arthur the aardvark's sister is equal to -du?
mojiganga2, the indefinite integral of -1/5 * e^u is -1/5 * e^(u) + c. I understand your logic and it would be true if "e" was a variable like "y" instead, but "e" is a constant rather than a variable. Think of it like the derivative of e^x is e^x as well as its integral is e^x. Hope this helps!
7:37 I think you forgot to take the integral. I think the answer would be (-1/5) (e^u+1/u+1)+c …. Please correct me if I am wrong
Argh. I stopped paying attention to what he said and started listening to the crow!
There was no need to take double substitution, but I think he did it in the case of more complicated problems. Thank you Sal!
no homo, i really do love this guy lol im one of his biggest fans and admire everything he does
holy shit tried that question before playing the video and got it right woo :D:D
THANK UUUUUUUUUU– lol get it. U-
THANK YOU!!!!!!!!!!!!!!!
You're never "forced" to use any type of substitution once you find patterns
Even though it's not mine, I would like to dedicate this video to Leonhard Euler. The disease in his eye did not prevent him from seeing in mathematics what those before him had missed. Thank you, Khan, and thank you, Euler.
obnoxious crow. lol
Your videos are very helpful when I forget how to do things like this!
I know you've been very busy today, but maybe sometime in the future, are there any examples where you are forced to do 2 substitutions and there is no way to do it in one?