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# Why did he divide by 2?? :/ Watch

1. Why was 2 divided by 2 & why was the same thing applied to 3?

Video:
https://youtu.be/eufqV0B6SP8?t=14m44s
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Why was 2 divided by 2 & why was the same thing applied to 3?

Video:
https://youtu.be/eufqV0B6SP8?t=14m44s
What happens when you differentiate ln(2x+1)?
3. (Original post by Gregorius)
What happens when you differentiate ln(2x+1)?
1/(2x+1)
1/(2x+1)
Now try integrating that and see if you get the same result as when you started...
1/(2x+1)
Uh uh; how does the chain rule go?
1/(2x+1)
d/dx ln f(x) = f '(x) / f(x)
Thus d/dx ln(2x+1) = 2/2x+1
Therefore Integrating 1/2x+1 would give [1/2 ln(2x+1) ] + C

As you are multiplying by a constant of 2, the integral turns in [2/2 ln(2x+1)] +C
7. (Original post by Gregorius)
Uh uh; how does the chain rule go?
y = Int where t= 2x+1
dy/dt= 1/t

dt/dx= 2

so 1/t x 2
1/(2x+1) x 2
2/(2x+1)
8. Same reason as before you need to make the top of the fraction f '(x) = 2
as the differential of u =(2x+1) is 2
you do this by
∫ 1/(2x+1) dx
= (1/2)∫ 2/(2x+1) dx
9. (Original post by Katiee224)
Now try integrating that and see if you get the same result as when you started...
(Original post by Gregorius)
Uh uh; how does the chain rule go?
(Original post by XOR_)
Same reason as before you need to make the top of the fraction f '(x) = 2
as the differential of u =(2x+1) is 2
you do this by
∫ 1/(2x+1) dx
= (1/2)∫ 2/(2x+1) dx
Okay I get it now Thank you!!
y = Int where t= 2x+1
dy/dt= 1/t

dt/dx= 2

so 1/t x 2
1/(2x+1) x 2
2/(2x+1)
This is where the error is
you don't times by dt/dx
you times by dx/dt

so it's
∫ 1/t x (1/2) dt
= (1/2)∫ 1/t dt
= (1/2)ln(t) + c
= (1/2)ln(2x+1) + c

^ this is without the constant 2 in the original question if there was a constant 2
it would be
= (2/2)ln(2x+1) + c
11. (Original post by XOR_)
This is where the error is
you don't times by dt/dx
you times by dx/dt

so it's
∫ 1/t x (1/2) dt
= (1/2)∫ 1/t dt
= (1/2)ln(t) + c
= (1/2)ln(2x+1) + c

^ this is without the constant 2 in the original question if there was a constant 2
it would be
= (2/2)ln(2x+1) + c
But am I not supposed to use the chain rule?
But am I not supposed to use the chain rule?
if you use t as a variable then
(dy/dt) = (dy/dx)(dx/dt)

which is how you get ∫ ..... dt
so
∫ 1/t (dx/dt) dt
where dx/dt = (1/2)

-> (1/2)∫ 1/t dt

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