HP Prime integration issue

02122021, 08:04 PM
Post: #1




HP Prime integration issue
Hello, when I try to integrate 1/(x^32) with respect to x, I see in my answer something with rootof(). When I try to retype this into the calculator, I receive a syntax error, presumably because the first argument has 6 parameters, and the second argument has 7 parameters. What does this even mean? What does this function even mean? There's clearly an elementary representation of this integral (just type it on wolfram alpha, for example). I can't even replicate or approximate the result because I get a syntax error when even pressing enter to see what it looks like in long form. What's happening here?


02122021, 10:53 PM
Post: #2




RE: HP Prime integration issue
Hi, LCieParagon
I asked this before, and you are not supposed to see rootof(...) in Prime. see https://www.hpmuseum.org/forum/thread11...#pid105773 For your example, we can do a simple substitution, x = 2^(1/3)*y, dx = 2^(1/3)*dy (y integral result copy/pasted from Hp Prime emulator) I = ∫(1/(x^32), x) = 2^(1/3)/2 * ∫(1/(y^31), y) = 2^(1/3)/2 * (atan((y+1/2)/(1/2*√3))/√3  1/6*ln(y^2+y+1) + 1/3*ln(abs(y1))) Back substitute y = x/2^(1/3), and we are done.  The reason for substitution is y^31 = (y1)*(yw)*(yw²), where w = exp(i*2*pi/3) 3/(y^31) = 1/(y1) + w/(yw) + w²/(yw²) I = 2^(1/3)/6 · ∫(3/(y^31), y) = 2^(1/3)/6 · (ln(y1) + w·ln(yw) + w²·ln(yw²)) 

02132021, 02:02 AM
Post: #3




RE: HP Prime integration issue
(02122021 10:53 PM)Albert Chan Wrote: Hi, LCieParagon “I’m not supposed to see this in Prime”, but I do see it, and it doesn’t make sense to me. I can use simple algebra to do this integral by hand and while it looks pretty ugly, it’s actually not difficult to do. I can’t even simplify it because one matrix has a 7 parameter argument, and one 6. I can’t replace the empty spot with a 0, else I receive a wrong answer. There is no literature on rootof function on the HP Prime. I consider this a bug and should be fixed. I’m a math professor and this result is less than useless to me especially when a competitor calculator computes it in seconds. 

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