#51 Integrating problem of (a*x + b)^n dx general format

open
nobody
None
3
2008-04-14
2008-02-24
Valer Gonda
No

When integrate a function of general format
(a*x + b)^n dx
Maxima doesn't use the simplest formula.

In case of integrating (a*x + b)^n dx Maxima should use:

(a*x + b)^(n + 1)
―――――――――――――――― to calculate.
a * (n + 1)

That is:
n + 1
⌠ n (a∙x + b)
⌡(a∙x + b) dx = ―――――――――――――
a∙(n + 1)

For example:
4
⌠ 3 (5∙x - 2)
⌡(5∙x - 2) dx = ―――――――――――
20

Discussion

  • Valer Gonda

    Valer Gonda - 2008-02-24

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    That is:
    n + 1
    ⌠ n (a∙x + b)
    ⌡(a∙x + b) dx = ――――――――――――――――
    a∙(n + 1)

    For example:
    4
    ⌠ 3 (5∙x - 2)
    ⌡(5∙x - 2) dx = ―――――――――――
    20

     
  • Barton Willis

    Barton Willis - 2008-02-26

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    With 5.14.0, I get

    (%i65) integrate((a*x + b)^n,x);
    Is n + 1 zero or nonzero? nonzero;
    (%o65) (a*x+b)^(n+1)/(a*(n+1))

    Isn't this the answer you wanted?

     
  • Raymond Toy

    Raymond Toy - 2008-02-26

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    Barton,

    Evaluate his test integral: integrate((5*x-2)^3,x);

    The result is not (5*x-2)^4/20, but slightly different.

    I don't consider this a problem.

     
  • Barton Willis

    Barton Willis - 2008-02-26

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    Oh, okay -- we have

    (%i1) integrate((5*x-2)^199,x);
    (%o1) (5*x-2)^200/1000

    (%i2) integrate((5*x-2)^3,x);
    (%o2) (125*x^4)/4-50*x^3+30*x^2-8*x

    Is there an option variable that controls the expansion of
    the integrand / antiderivative?

     
  • Raymond Toy

    Raymond Toy - 2008-02-26

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    Ah, found it. Look in diffdiv in src/sin.lisp.

    The first clause of the cond expression checks to see if the exponent is between 0 and 6 (exclusive). If so, it expands out the expression and integrates again. If not, it tries some other approach. Of course, there are no comments on why it does this and why 6.

     
  • Stavros Macrakis

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    Maxima can't guarantee to use the simplest formula. There are various tradeoffs made internally....

    Requesting that the result be in one form rather than another -- assuming they're both correct -- is a feature request not a bug report, so I have changed this item's type and lowered its priority.

     
  • Stavros Macrakis

    • labels: 840495 -->
    • priority: 5 --> 3
     

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