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# Integration Maths Problem

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1. Can anyone help me solve:
Int (sqrt(x+1)-sqrt(x))^(3/2) dx.
With substitution, it becomes of the form:

Int (cosh(y)-sinh(y))^(3/2)/sinh(2y) dy
or 1//2 Int exp(-3y/2)/(exp(2y)-exp(-2y)) dy

Even if you cannot integrate this function, ideas would be extremely helpful.
2. i managed to transform the last version into

int 1/(w8 - 1) dw

but am not sure what to do after that
3. Might I ask how you got that?
4. Wolfram Alpha cannot do this (at least in the amount of time I am entitled to on their servers!)
5. (Original post by Daaaaaaaaaaaaaaaan)
Might I ask how you got that?
i cannot reveal all the details due to TSR policy... but basically you let

w = ey/2
6. (Original post by Daaaaaaaaaaaaaaaan)
Can anyone help me solve:
Int (sqrt(x+1)-sqrt(x))^(3/2) dx.
With substitution, it becomes of the form:

Int (cosh(y)-sinh(y))^(3/2)/sinh(2y) dy
or 1//2 Int exp(-3y/2)/(exp(2y)-exp(-2y)) dy

Even if you cannot integrate this function, ideas would be extremely helpful.
I thought this forum had LaTeX support
7. (Original post by rhysowen)
I thought this forum had LaTeX support
LaTex support sounds like something Granny would purchase from Boots
8. (Original post by the bear)
i managed to transform the last version into

int 1/(w8 - 1) dw

but am not sure what to do after that
Assuming this is correct, you can write

w^8 - 1 = (w^4+1)(w^4-1) = (w^4+1)(w^2+1)(w^2-1).

Then .

Then some (painful) partial fractioning will finish things off.
9. (Original post by Daaaaaaaaaaaaaaaan)
Can anyone help me solve:
Int (sqrt(x+1)-sqrt(x))^(3/2) dx.
With substitution, it becomes of the form:

Int (cosh(y)-sinh(y))^(3/2)/sinh(2y) dy
or 1//2 Int exp(-3y/2)/(exp(2y)-exp(-2y)) dy

Even if you cannot integrate this function, ideas would be extremely helpful.
For
Use the following substitution

So

using

the

So

Now You can integrate this
10. Well done ztibor & DFranklin
11. Thank you

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