[Bug or Suggestion]About HP Prime G1 New Beta Firmware - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Calculators (and very old HP Computers) (/forum-3.html) +--- Forum: HP Prime (/forum-5.html) +--- Thread: [Bug or Suggestion]About HP Prime G1 New Beta Firmware (/thread-14031.html) [Bug or Suggestion]About HP Prime G1 New Beta Firmware - yangyongkang - 11-22-2019 08:37 AM I downloaded the latest HP Prime RC firmware， This is the information of my calculator Code: HP Prime: "HP Prime Graphing Calculator Software Version: 2.1.14341 (2019 11 20) BETA Hardware Version: A CAS Version: 1.5.0 Serial Number: 4CY3450CZZ Operating System: V0.050.640 © 2019 HP Development Company, L.P. " The following are the problems I encountered during use： (i) Code: plotfunc(x^ln(x)) Then click Show, the calculator restarts (ii) Code: int(atan(x)/(x^2*(1+x^2)),x) Hp prime didn't figure it out, this is the result of Wolfram Alpha (iii) Code: simplify((1/sin((π/18)))-(sqrt(3)/cos((π/18)))) Hp prime calculation result： Code: (-√3*tan(2/9*π)^4+√3-2*tan(2/9*π)^3-2*tan(2/9*π))/(2*tan(2/9*π)^3-2*tan(2/9*π)) Actually Code: evalf((1/sin((π/18)))-(sqrt(3)/cos((π/18)))) Hp prime calculation result： Code: 4 RE: [Bug or Suggestion]About HP Prime G1 New Beta Firmware - Albert Chan - 11-22-2019 06:03 PM (11-22-2019 08:37 AM)yangyongkang Wrote:  (ii) Code: int(atan(x)/(x^2*(1+x^2)),x) Hp prime didn't figure it out, this is the result of Wolfram Alpha For XCas, it needed a nudge: $${1\over x^2(x^2+1)} = {1 \over x^2} - {1 \over 1+x^2}$$ ∫ (atan(x)/(x^2*(1+x^2)) dx = ∫ atan(x) d(-1/x) - ∫ atan(x) d(atan(x)) Xcas> int(partfrac(atan(x)/(x^2*(1+x^2))),x) ﻿ ﻿ ﻿ ﻿ → -atan(x)^2/2 + ln(x^2)/2 - ln(x^2+1)/2 - atan(x)/x RE: [Bug or Suggestion]About HP Prime G1 New Beta Firmware - yangyongkang - 11-23-2019 02:18 AM In the process of using, I have encountered more troublesome indefinite points. (i) Code: ∫(e^atan(x)/(sqrt(x^2+1))/(1+x^2),x) Hp prime can't be solved directly, but through the following variant Code: subst(∫(e^atan(x)/(sqrt(x^2+1))/(1+x^2),x),x=tan(t)) In the old version of the firmware can be solved But the new firmware can't be solved (ii) Code: int(1/sqrt(x^3-x),x) Code: ∫(1/(1+x^4)^(5/4)) (iii) Code: ∫(x*e^x/(sqrt(e^x-1)),x) Hp prime can't be solved directly, but through the following variant Code: subst(∫((e^x*sqrt(e^x-1)*x)/(e^x-1),x),equal(x,ln(t^2+1))) get Code: 2*t*ln(t^2+1)*sign(t)-4*t*sign(t)+4*atan(t)*sign(t) RE: [Bug or Suggestion]About HP Prime G1 New Beta Firmware - yangyongkang - 11-29-2019 02:38 PM Related issues Code: ∫(∫(e^(-(x^2+y^2)/2),y,-(sqrt(a^2-x^2)),sqrt(a^2-x^2)),x,-a,a) The answer from XCAS Code: integrate(sqrt(pi)*1/(sqrt(2))*erf(sqrt(a^2-x^2)*exp(ln(2)/2)/2)*exp(-x^2/2)-sqrt(pi)*1/(sqrt(2))*erf(-sqrt(a^2-x^2)*exp(ln(2)/2)/2)*exp(-x^2/2),x,-a,a) In fact, we can get the correct answer through polar transformation. Code: ∫(∫(e^(-r^2/2)*r,r,0,a),x,0,2π) Get the answer Code: 2*pi*(-exp(-a^2/2)+1) RE: [Bug or Suggestion]About HP Prime G1 New Beta Firmware - yangyongkang - 12-04-2019 01:32 PM There are some other examples (i) Code: normal((simplify(int(e^(sin(x))*(x*cos(x)^3-sin(x))/cos(x)^2,x)))) xcas gets： Code: (x*exp(tan(x/2)/(tan(x/2)^2+1))^2*tan(x/2)^2-x*exp(tan(x/2)/(tan(x/2)^2+1))^2+exp(tan(x/2)/(tan(x/2)^2+1))^2*tan(x/2)^2+exp(tan(x/2)/(tan(x/2)^2+1))^2)/(tan(x/2)^2-1) Not the most simplified answer (ii) Code: int((sqrt(1+x^2)+sqrt(1-x^2))/sqrt(1-x^4),x) Code: int((sqrt(1+x^2)+sqrt(1-x^2))/sqrt(-1+x^4),x)