Dave

i tend to agree with blike on this one. the mentality of some people that post this stuff is somewhat bemusing at times. i can't remember exactly what Zarkov came up with now, but i've been reading the forums for a while before i actually started posting here the other day, and i believe it was something along the lines of spin gravity or something. now, i'm not a physicist by nature (i'm currently preparing to start a maths degree at Warwick), but i can tell what's right and what is fundamentally wrong. what probably astounds me more is people's acceptance to take this stuff in (especially when it's popularized so much by the media) even when significant evidence is provided to the contrary. i suppose, as you say, that is has something to do with people wanting to believe something different than the truth. one of the more famous ones is the NASA conspiracy that nobody actually landed on the moon, which i personally find quite amusing

hmm solve the differential equation dy/dx = what? it's not an equation otherwise

i was looking at this and just saw the bit about rationalising the numerator, which was a bit silly of me, but oh well. when you rationalize the numerator, you will get (as you say): (x^2+1)/(x*sqrt(x^2+1)) but you can split this up so that it becomes: :lint: (x/sqrt(x^2+1) + 1/(x*sqrt(x^2+1))dx the first bit is trivial (just substitute u^2 = x^2 + 1), and then the second bit is a bit more tricky, but i suspect a trig substitution like x=tan(t) might do it. well, you've got 2 separate approaches to doing it now at least

i think the worst possible thing that could be done would be to stopped manned space flights, especially since we now have the ISS up there, which is something that may provide us with the means to eventually get to other planets - which i believe is a pretty good cause in my own humble opinion

After more than 30 years in space heading away from Earth, Pioneer 10 has sent its last signal home. Pioneer's last, very weak signal was received on 22 January, after which US space agency (Nasa) engineers reported that its power source had decayed such that it might not be capable of sending another message. Following its encounter with Jupiter, Pioneer 10 explored the outer regions of the Solar System, studying the solar wind as well as cosmic rays from deep space. Since its official science mission ended on 31 March, 1997, Pioneer's weak signal has been tracked by Nasa's Deep Space Network as part of a new study of communication technology in support of a future Interstellar Probe mission. At last contact, Pioneer 10 was 12.2 billion km from Earth, or 82 times the normal distance between the Sun and the Earth. Read more at http://news.bbc.co.uk/1/hi/sci/tech/2802041.stm.

he explained it in rather complex terminology basically, if you have a function like cos(x), e^x or any function that has continuous derivatives, you can expand it in terms of x. a really crude way to think of it is kind of like a more complicated binomial expansion. you start of by presuming that some function of x, f(x) = a + bx + cx^2 + dx^3 + ... where a, b, c, d etc are constants. for example, if you take f(x) = e^x, then you can say when x = 0, a = 1. then by differentiating it, you can see that b = 1, then again to see that c = 1/2 and d = 1/6, e = 1/24, etc so therefore e^x = 1 + x + x^2/2! + x^3/3! + ... + x^n/n! you can test it in your calculator if you want, but it works. btw, this is a bit overly simplified, i've not really studied these things in detail, but this is the basic principle behind it.

oh, also, you can define arccosecant etc in terms of arcsin etc. say you have an equation: cosec(a) = b then a = arccsc(b) but also, 1/sin(a) = b then a = arcsin(1/b) but a = arccsc(b), so arcsin(1/b) = arccsc(b) you can do a similar thing for arcsecant and arccotangent, but it's all fairly useless

yeah, but they're fairly useless. e.g. if you have the equation: cosec(x) = 2 then it's pretty obvious that this is just the same as sin(x) = 1/2 and x = arcsin(1/2) = :pi:/6 so it's just another set of functions that don't really have too much use

[edit: btw, i have no idea whether this is right] i've had a go at it, and it seems approachable. what i did was to get your integral, :lint: sqrt(1+x^-2)dx then apply the subsitution: x = sinh(t) => dx = cosh(t)dt and then the integral becomes :lint: coth(t)cosh(t)dt which can be further simplified down to :lint: cosh^2(t)/sinh(t)dt then by making the substitution u = cosh(t), it then becomes :lint: u^2/(u^2-1)du then by dividing it out you get: s = u + artanh(u) and if you put the limits in i *think* it should work. i could be wrong however, but it looks like you'll get the right kind of answer, since artanh(u) can be written in log form. i've no idea how to do this without hyperbolic functions either hope this helps.