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qntty

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- Thread starter qntty
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qntty

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- #2

adriank

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I seem to remember reading that, in general, HP calculators do tend to expand polynomials before integrating, rather than perform a substitution if it's simple enough. I really doubt there's any way to tune how it integrates things.

As an example: [itex]\int (x + 1)^3 \,dx[/itex]. I'm guessing your calculator gives a result of [itex]\frac14 x^4 + x^3 + \frac32 x^2 + x[/itex]. (I'm not 100% sure; I read this before the 50g came out, but the 50g is fairly similar to the 49G.) However, both Mathematica and my TI-89 give [itex]\frac14 (x + 1)^4[/itex]. Note that this expands to [itex]\frac14 x^4 + x^3 + \frac32 x^2 + x + \frac14[/itex]; the result differs from the other one by a constant 1/4. (Hopefully this demonstrates the importance of the integration constant!)

- #3

qntty

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In your example, there is actually no obvious substitution that can make it easy to integrate with that method; indeed, both Mathematica and my TI-89 will expand it before integrating (and give a large mess as a result). There doesn't seem to be a nice general formula for the result (well, Mathematica can give one that uses hypergeometric functions, but it's not exactly pretty).

Yeah I didn't notice that, my example should have been [tex]\int (10x-8)^{40} dx [/tex]

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