[Bug or Suggestion]About HP Prime G1 New Beta Firmware

[yangyongkang]

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

[Albert Chan]

(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

[yangyongkang]

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)

[yangyongkang]

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)

[yangyongkang]

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)