11:55, wondering if you mixed up the (1-t)^(v-1) and the t^(u-1) here since you got f(t) = (1-t)^(-1/10) t^(-9/10) Which should be equal to B(u, v) for u-1 = -9/10 and v-1 = -1/10 if I look at the form above So B(1/10, 9/10) should be it so exactly the opposite way around as you did, or am I mistaken here and doesnt it matter? I have only barely learned the basics of complex analysis so forgive me if this is wrong
A friend threw this integral at me and I have no idea what to do. The solution isn't very nice he said but maybe one of you fellas wanna try: WA doesn't know either. I tried to expand the trig functions into their complex definitions but there is not a lot happening still :/ Integrate [ Cos[ x^2 Log(x) ] / (e^-Sin(x) Sqrt[ Cosh(x) ] ), {x,0,∞} ]
Hi bro, I’m a big fan of yours. I really enjoy watching your videos. I have one question for you. Um...how can I integrate (ln x)^x dx?? I can't solve it. Plz help me. Thanks
I=1/2•int[0,pi/2](sin^-4/5(Ø)ln(sin(Ø))cos^-6/5(Ø))dØ ß(u,v)=2•int[0,pi/2](sin^(2u-1)(Ø)cos^(2v-1)(Ø))dØ ðß/ðu=4•int[0,pi/2](sin^(2u-1)(Ø)ln(sin(Ø))cos^(2v-1)(Ø))dØ ß(u,v)=Ř(u)Ř(v)/Ř(u+v) ðß/ðu=Ř(u)Ř(v)(¥(u)-¥(u+v))/Ř(u+v) =(¥(u)-¥(u+v))ß(u,v) I=-5pi/4•csc(pi/10)(¥(1/10)-¥(0))/Ř(0) not sure if that converges
@Mustafa_ShahzadVideos is a popular format of reaching teaching very quickly, but books tend to last forever. While the talent isn't wasted on videos, it would be even more beneficial for all if the information was put on books as well.
"The Hindu religion is the only one of the world's great faiths dedicated to the idea that the Cosmos itself undergoes an immense, indeed an infinite, number of deaths and rebirths. It is the only religion in which the time scales correspond to those of modern scientific cosmology. Its cycles run from our ordinary day and night to a day and night of Brahma, 8.64 billion years long. Longer than the age of the Earth or the Sun and about half the time since the Big Bang." “Most cultures imagine the world to be a few hundred human generations old. Hardly anyone guessed that the cosmos might be far older but the ancient Hindus did,” "It is the only religion in which the time scales correspond, to those of modern scientific cosmology" ~ CARL SAGAN (famous astronomer, cosmologist)
Hi,
"Terribly sorry about that": 1:29, 1:57, 3:47, 6:57, 8:54
"Okaay, cool": 1:47, 11:29, 12:39
Next thing you know bros gonna be solving a 4th order de
Dont give him ideas....
Seeing our boy Kamal struggling with drawing the [ ] is the best thing in 2025❤❤
Hi,
"terribly sorry about that" : 1:30 , 1:57 , 2:00 , 3:47 , 6:58 , 8:56 ,
"ok, cool" : 1:47 , 4:34 , 7:54 , 11:29 , 12:41 .
*Happy New Year! Excellent work!*
From about 4:00, you can just use the Mellin transform of ln(1+x) by letting 1/x^2=t and get your final result right away.
The suspense over how we get rid of that ⁵√tan is killing me. 😂
I wonder if this integral has a general solution for different root values. Maybe you could make a video about it. 🤔
11:55, wondering if you mixed up the (1-t)^(v-1) and the t^(u-1) here since you got
f(t) = (1-t)^(-1/10) t^(-9/10)
Which should be equal to B(u, v) for u-1 = -9/10 and v-1 = -1/10 if I look at the form above
So B(1/10, 9/10) should be it so exactly the opposite way around as you did, or am I mistaken here and doesnt it matter? I have only barely learned the basics of complex analysis so forgive me if this is wrong
Beautiful result , loved every minute i hope for more videos .
Starting the year with a beautiful trig integral nice!
Nice integral ❤
Very nice. Thanks
يا جنونك يا مستر وائل مينفعش كده
Good method to solve this complicated integration, Thank You for video Kamaal
Terrifying trig integral: Exists
Bounds being 0 to pi/2: not so terrifying now!
Very nice💯💥
Thanks for this awesome integral that ends the year 2024.
How can I learn calculus 1, any online resources?
3blue1brown's series is quite good for intuition buildig
@@rishabhshah8754 thanks, i will look into it
Khan academy
A friend threw this integral at me and I have no idea what to do. The solution isn't very nice he said but maybe one of you fellas wanna try:
WA doesn't know either.
I tried to expand the trig functions into their complex definitions but there is not a lot happening still :/
Integrate [ Cos[ x^2 Log(x) ] / (e^-Sin(x) Sqrt[ Cosh(x) ] ), {x,0,∞} ]
Make video on integral includin' the concept of
Z transformation
Hi bro, I’m a big fan of yours. I really enjoy watching your videos. I have one question for you.
Um...how can I integrate (ln x)^x dx?? I can't solve it. Plz help me. Thanks
yo I'm kinda new to integration; how do we know that the result using sin²θ will give us 1/2 of the result using sinθ?
The power property of logs: log(a^p) = p log(a)
@Empisee ohhh right 😭 tysm
One day center equation results happiness and much positivities. Substantial happiness and durable exponent.
👏👏👏👍
2025 starting off strong
I=1/2•int[0,pi/2](sin^-4/5(Ø)ln(sin(Ø))cos^-6/5(Ø))dØ
ß(u,v)=2•int[0,pi/2](sin^(2u-1)(Ø)cos^(2v-1)(Ø))dØ
ðß/ðu=4•int[0,pi/2](sin^(2u-1)(Ø)ln(sin(Ø))cos^(2v-1)(Ø))dØ
ß(u,v)=Ř(u)Ř(v)/Ř(u+v)
ðß/ðu=Ř(u)Ř(v)(¥(u)-¥(u+v))/Ř(u+v)
=(¥(u)-¥(u+v))ß(u,v)
I=-5pi/4•csc(pi/10)(¥(1/10)-¥(0))/Ř(0)
not sure if that converges
You should write books on integral calculus and integration,bro.
Don't waste your talent.
I wouldn't say he's wasting his talent. I love his videos, but if he wrote a book i know for sure i wont read it. I just dont really like to read.
He's making videos, not all teaching talent has to be expressed through books you know
@Mustafa_ShahzadVideos is a popular format of reaching teaching very quickly, but books tend to last forever. While the talent isn't wasted on videos, it would be even more beneficial for all if the information was put on books as well.
"The Hindu religion is the only one of
the world's great faiths dedicated to
the idea that the Cosmos itself
undergoes an immense, indeed an
infinite, number of deaths and
rebirths. It is the only religion in which
the time scales correspond to those of
modern scientific cosmology. Its
cycles run from our ordinary day and
night to a day and night of Brahma,
8.64 billion years long. Longer than
the age of the Earth or the Sun and
about half the time since the Big
Bang."
“Most cultures imagine the world to be a few hundred human generations old. Hardly anyone guessed that the cosmos might be far older but the ancient Hindus did,”
"It is the only religion in which the time scales correspond, to those of modern scientific cosmology"
~ CARL SAGAN (famous astronomer, cosmologist)