[Bug or Suggestion]About HP Prime G1 New Beta Firmware
11-22-2019, 08:37 AM
Post: #1
 yangyongkang Member Posts: 51 Joined: Dec 2018
[Bug or Suggestion]About HP Prime G1 New Beta 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

study hard, improve every day
11-22-2019, 06:03 PM
Post: #2
 Albert Chan Senior Member Posts: 2,231 Joined: Jul 2018
RE: [Bug or Suggestion]About HP Prime G1 New Beta Firmware
(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
11-23-2019, 02:18 AM (This post was last modified: 11-23-2019 02:27 AM by yangyongkang.)
Post: #3
 yangyongkang Member Posts: 51 Joined: Dec 2018
RE: [Bug or Suggestion]About HP Prime G1 New Beta Firmware
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)

Attached File(s) Thumbnail(s) study hard, improve every day
11-29-2019, 02:38 PM
Post: #4
 yangyongkang Member Posts: 51 Joined: Dec 2018
RE: [Bug or Suggestion]About HP Prime G1 New Beta Firmware
Related issues
Code:
∫(∫(e^(-(x^2+y^2)/2),y,-(sqrt(a^2-x^2)),sqrt(a^2-x^2)),x,-a,a)
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)
Code:
2*pi*(-exp(-a^2/2)+1)

study hard, improve every day
12-04-2019, 01:32 PM
Post: #5
 yangyongkang Member Posts: 51 Joined: Dec 2018
RE: [Bug or Suggestion]About HP Prime G1 New Beta Firmware
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)

(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)

Attached File(s) Thumbnail(s) study hard, improve every day
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