Integral of 1/(1+e^x)

Integral of 1/(1+e^x) in one minute #shorts #calculus #afternoonintegral

#shorts
bprp x

[__python__]

You can also multiply the numerator and denominator by exp(-x)...

[fjfrjrjewjfkrjejejw]

يحل بطريقتين مختلفتين هما 1- سحب مشترك e^x من المقام من لاشيء ثم ننقل e^x للبسط فيصبح مقام مشتقته فوق منه
2- اضرب بكسر مكافئ e^-x واقسم على e^-x فيصبح مقام مشتقته فوق منه

[enricorossi]

U-sub works anyway, you just have to use partial fractions too

[GGA]

In this vídeo the only thing that I learned was that we should subscribe for more 😮

[tarfaibrahim]

Wow ....when see it u think complicated when he solves u feel its piece of cake ..I wish if I had him as my teacher when I was in 12th grade ....he may make in general my basics in math were weak but now I am better 😅with practice

[christianmosquera]

Excellent video wonderful 😊😊😊😊😊😊😊❤❤❤❤❤❤❤

[MazenHamad]

We multiply both the numerator and denominator by e^_x

[makakh]

So this integral i solved with my teacher in class and it also came from 0 to 1 in the exam but the way we did it i find it easier multiply by -e^-x than the anti derivative is -ln(1+e^-x) after pluging the values you get 1+ln(2)-ln(1+e) approximately 0.38

[biscuit_]

this is exactly what I got stuck with thx

[scooby]

I like how he switches the markers like a magician! 😅

[econcrook]

Long divide 1+e^x into 1, which goes in once and leaves a remainder of - e^x/(1 + e^x). Then integrate the same way blackpenredpen did toward the end

[chiprollinson]

let e^x=tan^2(y)... answer ends up in the form 2*ln(sqrt(e^x)/sqrt(e^x+1)) +C which looks more complicated. :)

[shashankdesai]

Divide by e^x on both numerator and denominator then integrate directly

[theknightikins]

I don't know why but adding e^x and then immediately subtracting e^x looked really funny to me

[mahmoudaboualfa]

Another way:
Integral dx/(1+e^x) = Integral e^-x/(1+e^-x) dx = -ln(1+e^-x) +c = ln(e^x/(1+e^x) +c = ln(e^x) - ln(1+e^x) +c = x - ln(1+e^x) +c
Note: last three steps can be eliminated if you're good at integrals. But the one present in the video is faster and easier to perform for those who don't want to use negative powers.

[abhinavshourya]

They seem to think about poke with a speaker

[qiangli]

math is interesting, equations make it easy, although i can not follow his words😂

[Ragehunter]

Damn now I understand, very nice one 😅😂

[Kettwiesel]

That's the true dual wield: black and red pen