∫−sin(x)*(cos(x))^7dx wrong answer? [SOLVED]

[vvolkan]

I share screenshots wolfram alpha and hp prime pro (additionally, after trig->cos rewrite function) screenshots.

[Arno K]

The prime usually omits this constant as you can see when you enter a simple integral like int(x,x) which outputs 1/2*x^2, the 1/8 constant results from your trig->cos.
Arno

[vvolkan]

Hi Arno, how should i enter the integral to get the most proper "cos^8(x)/8" result? I tried this calculation on some other calculator softwares all give "cos^8(x)/8" besides hp prime.

[Arno K]

I don't know a way to do so, on the 50G there was a flag to prefer sine or cosine, if I remember correctly but even here you have to know what you want.. Perhaps Mr. Parisse can give deeper insight.
Arno
Edit: but this doesn't make the 50G give your desired resolt

[parisse]

Run ∫−(cos(x))^7*sin(x) (product argument reversed).
The integration algorithm tries to detect a f'(u)*u' form, the first one detected that works is used. Here you could use u=cos(x) or u=sin(x), both work (once you rewrite cos(x)^6 as (1-sin(x)^2)^3). Reverting the arguments will select the other possible u.

[Aries]

(05-25-2018 10:09 PM)vvolkan Wrote:  Hi Arno, how should i enter the integral to get the most proper "cos^8(x)/8" result? I tried this calculation on some other calculator softwares all give "cos^8(x)/8" besides hp prime.

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Best,

Aries

[Arno K]

Well, I don't bother other calculators, and the integral above is not one of those I use a calculator for as the necessary substitution can easily be seen, I do things like that by hand (here: in head), I had seen this topic and so gave it a try on the prime and the 50G as well.
Arno

[Aries]

(05-26-2018 07:29 AM)Arno K Wrote:  Well, I don't bother other calculators, and the integral above is not one of those I use a calculator for as the necessary substitution can easily be seen, I do things like that by hand (here: in head), I had seen this topic and so gave it a try on the prime and the 50G as well.
Arno

Im with you, Arno
Best,

Aries

[parisse]

to Aries: I guess the TI nspire does not try as many transformations than the HP.
Therefore simple exercices (that can be solved in your head) might return a more complicated answer on the HP because the HP algorithm tries a rule that the TI does not try. But when you get an answer on the HP and nothing on the TI, you are happy to have the HP. For example sin(x)^2*cos(x)^2*exp(x). Or (2x^2+1)*exp(x^2).

[vvolkan]

(05-26-2018 01:40 PM)parisse Wrote:  to Aries: I guess the TI nspire does not try as many transformations than the HP.
Therefore simple exercices (that can be solved in your head) might return a more complicated answer on the HP because the HP algorithm tries a rule that the TI does not try. But when you get an answer on the HP and nothing on the TI, you are happy to have the HP. For example sin(x)^2*cos(x)^2*exp(x). Or (2x^2+1)*exp(x^2).

I agree. Hp can give the same result. The issue is that to know/learn how to use it.