Maths: Integrating (sqrt(x+1)-sqrt(x))^(3/2)dx

[dan876654]

Maths: Integrating (sqrt(x+1)-sqrt(x))^(3/2)dx.
It can be substituted to form:

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

[factor-fiction]

Are you telling us or asking us?

[HowardKennitby]

No point asking me.

[dan876654]

Asking, please.

[vascop]

I have done the proof, but i think your result contains an error:
INT((cosh(y)-sinh(y))^(3/2))/sinh(2y))dy.
or
1/2 INT exp(-3y/2)/(exp(2y)-exp(-2y)) dy

This should be:

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

The division sign (/) has been removed.
I will post a reference to my proof a bit later today.

[factor-fiction]

Yes, substituting sin or sinh or cos or cosh is a good way of integrating equations of that form.
I haven't got time to check it (I'm a bit rusty on this) but I'm sure from experience that vascop will be right

[vascop]

Here is a link to my solution.
You should be able to download it. It is a pdf file.
https://docs.google.c...1BTNjZJSHpia2h3akU5QQ

[vascop]

Where are you Dan?

[vascop]

Sometimes you just wonder if it's worth answering some people's questions. They ask a complicated question, you put in a lot of effort to answer them and then they just ignore your answer. No manners some people!