Solving an integral of an integral

Creating an integral of an integral. The integral of tan^-1(x) is left as an exercise.

bprp #shorts #calculus #apcalculus #satisfying #oddlysatisfying #mathteacher #ASMR

[livingcodex]

No idea what you just did, but it looked kinda cool

[kelv_kei]

dx at the top and dx on the bottom cancel
integral sign at the top and integral sign on the bottom cancel
therefore
= (tan^-1 x)/(tan^-1 x)
= 1 + c (never forget the c)

[tspiker]

The anger and fury I feel watching you write on paper with dry erase markers cannot be fully expressed with words.

[omjoglekar]

for others out there who want to investigate the property :

intgeral f'(x)/f(x) = log ( f(x) ) + c if you didnt know

[themightyblueshell]

You should create more integral questions where you solve it by turning something into a integral and using u-sub.
Practically we just solved integral of (arctan(x))/(x*arctan(x) - (1/2)ln(1+x^2) + C)dx

[johnnyp]

I appreciate you so much bc you remind me that I shouldn’t overthink!

[NonTwinBrothers]

He should totally do a main channel vid about this lol

[zza]

You could go further by calculating the integral of arctan (by part)

[aditya_lord_of_darkness]

No what matter what you do never forget "+ C"

[dikshantubale]

Incase anyone dont know how to integrate do it by by parts consider second function to be 1

[gamechanger]

Teacher be like:
You still have to solve further and solve for int of tan′¹ so there we go
0 marks for you

[siddharthabanerjee]

Sir please give a quick tutorial of basic calculus used for physics

[thaopham]

This is one of the greatest integral I ever seen😅😅😂😂

[silvally]

When the teacher thinks the question isn't hard enough.

[basil]

Is this how mathematicians go about solving non elementary integrals to check for possible solutions.

[Shmizzad]

Anyone else notice he wrote “Stan” 3 times?

[nicktheswampert]

Do you just leave it like that or calculate the integral at the end

[herbcruz]

Then we can integrate the inverse tangent function by using Integration By Parts.

[parthbhave]

I would not have proceded before solving tan-1 integral

[devaorios]

Though I wanted to run this by you, int(tan^-1x) could be done by parts right? like we can take it to be 1xtan^-1x and integrate it. Not sure tho 😅