Integral of Sqrt (tan (x)) - (Hardest Integral, Easiest Solution!)

Jesus Christ is NOT white. Jesus Christ CANNOT be white, it is a matter of biblical evidence. Jesus said don't image worship. Beyond this, images of white Jesus are not just blasphemous and criminal, white Jesus is from Satan ( the imposter.) Why? Let's look at what Satan does:
1) He is incredibly narcissistic and promotes himself shamelessly.
2) He misleads and confuses.
3) He pushes people away from Jesus Christ God, the Holy Trinity, the one and only messiah. White Jesus does all three of the above and more -- matching the ways of Satan.

Statues of Christ are equally offensive to God the Christ. While money is the biggest idol, Jesus spoke sufficiently against carved images.
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You can also find me on Tik Tok @reuslovesmath and @polarpiny

In this video, I do a very short solution to a very hard integral. The integral of the square root of tangent of x. Integral root tan x. Integral sort(tan(x)). Fun challenging integrals part 1 begins here. (root tan x integral) or (root tan xi integral). root tanx

[chrysfredi]

I saw a random meme about this and didnt expect anything bad as i searched this out of couriosity... Today i lost my innocence

[syed]

I=int(sqrt(tanx))
Now cosider a new integral J
J=int(sqrt(cotx))
I+J=Int.(sqrt(cotx) + sqrt(tanx))
I+J=sqrt(2)*Int.( (sinx+cosx)/sqrt(sin2x))
we know that sin2x = 1-(sinx-cosx)²
I+J=sqrt(2)*Int.(
Now substitute sinx+cosx=t
(cosx+sinx)dx=dt
I+J=sqrt(2)*int.( dt/(sqrt(1-t²))



NOW
I-J=Int.(sqrt(cotx) - sqrt(tanx))
I-J=sqrt(2)*Int.( (sinx-cosx)/sqrt(sin2x))
we know that sin2x = (sinx+cosx)²-1
I-J=sqrt(2)*Int.(
Now sinx+cosx=t
(cosx-sinx)dx=dt
(sinx-cosx)dx=-dt



J-I=sqrt(2)*ln|x+sqrt(x²-1)|+ c2

Subtract them -2I=

[oliverhees]

take a shot every time he says "Yeah? Cool."

[DT_Worlds_Strongest_Goth]

"Fun"
"Integral of square root tan x"

Pick one lol

[michaellarson]

You can do it easier if you factor u^4+1 as Then you can preform partial fractions and trig substitution.

[pacman]

Cheers from Caracas Venezuela. Could can ask that application use for show this video?

[uniqueshood]

man . back in my days when there was no internet facility . i spent hours trying to solve these problems, yet could not solve .and now the students get these so easily . i feel jealous

[andreea]

i love your explanations, you make it really easy to understand!!

[PunmasterSTP]

How would you even figure all this out on your own for the first time?

[silentintegrals]

Great Video! Solving integrals si allways fun!

[MarkMcDaniel]

2u^2 =/= (u^2+1)(u^2-1). Please explain how you split the u-subbed integral?

[mlgamer]

I still haven't understood how the integral of (2u^2)/(1+u^4) transforms into integral of(u^2+1)/(1+u^4) + integral of (u^2-1)/(1+u^4). Can someone please help me with this??

[jackkalver]

Sometimes it’s easier to derive the substitute from its derivative.

[madd_maxx]

Can you do partial fraction decomposition with square roots in denominator

[Rafi_Ul_Hasan]

Watch a lot of video about it. But this is really awesome.. Thanks bro

[Varde]

Thank you very much. I was working on this the other day and I'm glad to know that there's another way of getting the solution.

[lex-fr]

I think you missed the parentheses for dv and dw

[apunbolaapun]

Can anyone tell me the sofware he is using???

[Indrani_Mukherjee]

Hey there ..you could've taken tanx =t^2 and then differentiated to get to dx and then carried on likewise ..it would have reduced the step where you took tan inverse on both sides! But apart from dad it was exactly what I was doing and it helped

[ernestschoenmakers]

The other method is partial fractions.