Integral of 1/(sqrt(x+1)+sqrt(x))

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How would u integrate this?
Integral of 1/(sqrt(x+1)+sqrt(x)),
integral by using conjugate,

blackpenredpen,
math for fun,

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I feel like there's a pewdiepie reference in the title lmao.

kidtherookie

>Puts "u" in title
>doesn't use a substitution with "u"

He's a tru mad man

ShinySwalot

BUT CAN YOU DO THIS? *flips chair back* nice video! blackpenredpen > pewdiepie

jadewolf

Slowly reminding me of all the calculus I've learned over the years. Was a nice "OH YEAH" when you multiplied by the conjugate.

rb

ok, so i don't need $399 to do this.

yashsingh

I'm happy for u, ull get 100k subscribers soon...u deserve the best

housamkak

If you make it a definite integral from 0 to 159734 you get 399.

Not sure if the title was a PewDiePie joke, but if it was you'll appreciate this.

winnablebtw

It took me 1 second to get the idea of "removing" the sqrts out of the denominator by using (a+b)*(a-b)=a^2-b^2, then I saw immediately that both of the x will cancel out each other - denominator gone and ready to integrate! Yaaay I'm so proud of myself! :-P

novidsonmychanneljustcomme

i really like your videos, they show the fun in mathematics.

MRealKing

Multiply by conjugate, from there on its easy

SteamPunkLV

Did I just watch the easiest Intergral on the planet?

Sid-ixqr

brpr did eat a troll recently, apparently

AndDiracisHisProphet

of course. I did a trig substitution with tan and sec, ended up doing a conjugate anyway except with trig.

wherestheshroomsyo

Awesome length. Thanks for all gr8 videos.

Kronis

You should custom set your camera's exposure, cause when your black shirt is in the middle of the screen, the video is bright, but when you leave the frame, the white whiteboard leads to the video being dark

VaradMahashabde

2/3[(x+1)^(3/2)-x^(3/2)] by rationalizing the denominator!

paraskhosla

And then I ended up distracted calculating upper and lower bounds of square roots algebraically for a half hour.
8 80/261<sqrt(69)<8 85/277 was one of my results.

paulfoss

B4 watching: rationalize, then integrate

thephysicistcuber

At first i tried x=tan^2x, then after I saw secx+tanx in the denominator i knew I had to go back and do what you sir did in the video :D

kaszimidaczi

Request to @blackpenredpen: Try to find the EXACT value of sin(pi/7 rad)!

einsteingonzalez

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