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106/1000, sometimes, let u equal the whole square root part

• bprp calculus b… 오래 전 2026.08.21 16:00 인기
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이전글? 더 좋은 수업을 위해, 선생님들도 끊임없이 배우고 성장합니다.2026.08.21
다음글나를 서울대로 보내준 공부 루틴2026.08.15
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@TannuBhardwaj-… 　오래 전

Day106?

2026-08-21 20:39

[ytcid:UgyLS22qWx4Dn4LbDY94AaABAg] Day106?



@Bhavya-f3u 　오래 전

??

2026-08-21 20:22

[ytcid:Ugx_l5LI0T6C_YhYsxp4AaABAg] ??



@Primalory 　오래 전

i don't understand why you don't put the +C before going back to the x world, that makes the equality wrong

2026-08-21 19:46

[ytcid:Ugxf2g16NxXPhnuAt_h4AaABAg] i don't understand why you don't put the +C before going back to the x world, that makes the equality wrong



@Bayerwaldler 　오래 전

I don’t see that it’s easier. Let u=x-1. Then x(x-1)^1/2 = (u+1)u^1/2 = u^3/2 + u^1/2, dx=du. It’s straightforward from that point on.

2026-08-21 19:14

[ytcid:Ugw87qnfMA4PJ2bHrKl4AaABAg] I don’t see that it’s easier. Let u=x-1. Then x(x-1)^1/2 = (u+1)u^1/2 = u^3/2 + u^1/2, dx=du. It’s straightforward from that point on.



@MisterJackTheA… 　오래 전

One day he'll forget the +C, even for just a second.

2026-08-21 18:20

[ytcid:UgzvfWUyOMlOGweyZeJ4AaABAg] One day he'll forget the +C, even for just a second.



@kamalajaiho567… 　오래 전

This question just like NCERT textbooks question i am feel that I were solve this type questions in my calss 12 time

2026-08-21 18:15

[ytcid:UgzD4WgriOV-vZIkYdB4AaABAg] This question just like NCERT textbooks question i am feel that I were solve this type questions in my calss 12 time



@TCARK_티-시-아르크 　오래 전

Nice!

2026-08-21 17:56

[ytcid:UgzJVJOKyALHnjEo09l4AaABAg] Nice!



@vikramrawat526… 　오래 전

Day 106

2026-08-21 17:52

[ytcid:UgxazUodjOu4P7C2Rkl4AaABAg] Day 106



@STARIslamicPar… 　오래 전

Nice explanation

2026-08-21 17:22

[ytcid:Ugz18sFcVJ7ADpEaOyN4AaABAg] Nice explanation



@BSky2025 　오래 전

I love it ?❤️

2026-08-22 07:49

[ytcid:Ugx0ubRvaLHSIJBJbdJ4AaABAg] I love it ?❤️



@TahaHashir-o5g 　오래 전

The Council invites you

2026-08-22 06:38

[ytcid:UgyZX9H5dIu10IAYqIZ4AaABAg] The Council invites you



@matthewfeig562… 　오래 전

Pretty easy to just set u=x-1. The integral becomes Int [(u+1) sqrt u] du = Int [u^(3/2) + u^(1/2)] du.

2026-08-22 04:28

[ytcid:UgxAqb4lWMkoLOBEUit4AaABAg] Pretty easy to just set u=x-1. The integral becomes Int [(u+1) sqrt u] du = Int [u^(3/2) + u^(1/2)] du.



@Necroplantser 　오래 전

i tried not using substitution or IBP

x√(x-1)
= (x-1)√(x-1) + √(x-1)
= (x-1)^1.5 + (x-1)^0.5

and the rest is history :D

2026-08-22 01:44

[ytcid:UgxhgujoQNqb_wEQa3t4AaABAg] i tried not using substitution or IBP x√(x-1) = (x-1)√(x-1) + √(x-1) = (x-1)^1.5 + (x-1)^0.5 and the rest is history :D



@russelltaylor7… 　오래 전

x√(x-1)dx
u=√(x-1)
u²=x-1
x=u²+1
dx=2udu
x√(x-1)dx is replaced by (u²+1)u×2udu=
2u²(u²+1)=2u⁴+2u²=2u⁵/5 +2u³/3 + C

(2/5)(x-1)^(5/2) + (2/3)(x-1)^(3/2) + C

(x-1)^3/2 + (x-1)^1/2=(x-1)½[x-1+1]=x√(x-1) ✔️

so x√(x-1)dx
 = (2/5)(x-1)^(5/2) +(2/3)(x-1)^(3/2) + C

2026-08-22 00:44

[ytcid:UgzurpN9YppjBGPQfTZ4AaABAg] x√(x-1)dx u=√(x-1) u²=x-1 x=u²+1 dx=2udu x√(x-1)dx is replaced by (u²+1)u×2udu= 2u²(u²+1)=2u⁴+2u²=2u⁵/5 +2u³/3 + C (2/5)(x-1)^(5/2) + (2/3)(x-1)^(3/2) + C (x-1)^3/2 + (x-1)^1/2=(x-1)½[x-1+1]=x√(x-1) ✔️ so x√(x-1)dx = (2/5)(x-1)^(5/2) +(2/3)(x-1)^(3/2) + C



@julianheller27… 　오래 전

Dieses Integral könnte man auch mit der partiellen Integration lösen. (D: x ;
I: √(x-1)). Aber etwas unangenehm mit den neuen Exponenten 3/2 und 5/2.

2026-08-22 00:42

[ytcid:Ugxqo8URLkJttyPjp7d4AaABAg] Dieses Integral könnte man auch mit der partiellen Integration lösen. (D: x ; I: √(x-1)). Aber etwas unangenehm mit den neuen Exponenten 3/2 und 5/2.



@brainfellow514… 　오래 전

That was actually easier than it looked.  Nicely done.

2026-08-21 22:34

[ytcid:UgyIxioqJwMmoe_4q8Z4AaABAg] That was actually easier than it looked. Nicely done.



@davidmilhousca… 　오래 전

What happens to the exponents? Why/how does it work?

2026-08-22 11:02

[ytcid:UgwiCtxys2n1yPUGbBl4AaABAg] What happens to the exponents? Why/how does it work?



@Mr.Chickem 　오래 전

Do I have to memorize all the series tests

2026-08-22 10:12

[ytcid:UgyQ1IWnF9DNx87Ubjd4AaABAg] Do I have to memorize all the series tests



@Tetraverse 　오래 전

Please make content on probability theory for one of these

2026-08-22 09:36

[ytcid:UgzW07qGGHtBKGlsjB14AaABAg] Please make content on probability theory for one of these