Completing the Square for Integrals

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

Here are a few more HARDER fun great integrals.

1) Integral of Sqrt(tan(x))

2) Integral of Arcsin(Sqrt(x))

3) Integral of e^(-x^2)

4) Integral of 1/(x^6+1)

[rickybobby]

nice example, but at time 7:45 and after you crossed out the u, you forgot to take the half outside.

[joshuasorber]

2:30 Where did you get the radical 2 in the denominator ? It's not really clear what happened there..

[davidkippy]

After you complete the square, substitite u for x+2. The numerator becomes u-2 and the denominator becomes 2 + u^2. Then just split the fraction, resulting in an arctan and another substitution leading to ln.

[morgard]

If you encounter some harder to complete to square quadratic polynomial you don't have to take out the "a" coefficient, just do this: ax^2+bx+c; join the square root of "a" -> (✓(a)x + ___)² and then divide the second term by it and multiply by the half of "b" -> (✓(a)x + b/2 × 1/✓(a))², so for example: 3x^2+4x+1 = (✓(3)x + 2/✓(3))² and you are done, now just complete it by adding the rest, so you need to get from 4/3 to 1 -> subtract 1/3 and you finally get (✓(3)x + 2/✓(3))² - 1/3. One more example: 5x^2 + 3x + 2 = (✓(5)x + 3/(2√(5)))² + 31/20.

[adrianpetersonguera]

I haven't even started Differential Calculus, but I'm so excited for this subject!

[TheJohnny]

I think you forgot to write 1/2 factor at 7:47 when you simplify terms, which affects the final result, otherwise nice video

[andresmoreno]

Iré a un maratón de integrales, me recomiendan algún libro para practicar?
Buen vídeo

[lich]

someone knows the method for integrals with several sin and cos functions where variable x is changed for tan(t/2) (or something like that, i dont remember clearly)?

[ChristGodinyouItrust]

Thank you so much for spotting that btw, Ricky!

[thomaselder]

I enjoy your videos. It would be nice if you had them organized into playlists though. Thanks.

[MrKk]

which pen mouse did you use to create the video??

[chocolatedud]

I’m in algebra😂😂 I should be in geometry though

[mamapeks]

im just 12yrs old, and i'm now im studying advanced calculus