Скачать или смотреть 🎤 Rapping the Integral of sec x 🔥

we integrate sec(x) with the power of fire bars 🔥 #mathsong

Check out all my math songs in this playlist:    • Math Songs  

the only thing better than a math speedrun is a math speedrhyme 🎤
what math song should I do next?

Destroying blackpenredpen's Proof Speedrun:    • Destroying blackpenredpen's Proof Speedrun...  
Turning Dr Peyam's pi^e vs e^pi Rap into a Banger:    • Rapping pi^e vs e^pi Like Dr Peyam  
Rapping the Integral of (sinx+cosx)/(sinx*cosx):    • Rapping the Integral of (sinx+cosx)/(sinx*...  

#Calculus

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LYRICS:

Are you up for the challenge? The types of integrals that enchant
Let’s review the integral of secant
Upon inspection you may not see any direction
But this integral stuff’s all about making correct connections
Obvious answers - they’re nice - but we don’t always have to have it
Let’s consider the derivative of secant while we’re at it
It’s itself but with an extra factor, sitting by a tangent
But hold up, this gives me an understanding of expansion
It’s not just that tangent is in secant’s derivative
But secant is in tangent’s this attachment is duplicative
So if we were to say, differentiate, secant plus tangent, what would that then create
Well it’s secant times tangent plus secant times secant
Can we factor out a secant? Heck yes we can
It’s secant times secant plus tangent, put in a pair
So secant plus tangent is here, but also there
Hey - give it a name, call it u, and we get room to spare
Speaking of things to spare, I hope we've got time
Let's save some and call the derivative of u u prime
So u prime is u times secant x
Divide by u to solve for secant x next
My rhymes leave you riveted
This secant x equals u divided into its own derivative
That's indicative, begin to clear away the fog
It's as if we differentiated u's natural log
So secant x equals d / dx of the log of secant plus tangent x
But all along we wanted secant's integral
Let's integrate both sides - fundamental principle
This integral of secant - that's we want
Integral of a derivative, these parts cancel and depart
Natural log of secant and tan, hand in hand bonding like close correspondents
And to top it off we add the arbitrary constant