Actually the question is, in some sense, wrong. What you should be doing (I hope you will consider this as constructive) is look for integrands of the form constant* f(u)^p*du.
That includes 3*(4+5*x)^6 but also 7*(8+9*x^2)^p * x and even (1+2*sin(x))^p*cos(x). this is one part of a "derivative-divides" integration system. You can look for a product where there is a power of a function of x, f(x)^p. See if diff(f(x),x) divides the rest of the product evenly [giving you the constant]. and then you know the integral is f(x)^(p+1)/(p+1) times the constant. (special case for p=-1 is log...) This is so much more powerful, and yet easy to explain, and probably no harder to program, that you should be doing this instead. If you want to see how to do this, in a half-page of code, and much much more in 2 pages, see this.. http://people.eecs.berkeley.edu/~fateman/papers/partition.mac and read the documentation, in a link on line 5 of that. RJF On Thursday, June 9, 2016 at 5:17:08 PM UTC-7, Aaron Meurer wrote: > > If p is an integer, you could just factor() the expression and pattern > match against it (or to guard against slow negatives, use sqf_list, > which is basically what your technique uses). Integration should work > for any p, though, non-integer or symbolic, so long as it doesn't > depend on x. So I would recommend: > > - factor() the expression in case it is expanded > - pattern match with Wild() and match() (or whatever it is > manualintegrate already uses) > > More general cases, say if p is a sum and the term is expanded, may > require further simplification functions like powsimp() to bring it > into canonical form. > > Aaron Meurer > > > On Thu, Jun 9, 2016 at 5:24 PM, Richard Fateman <[email protected] > <javascript:>> wrote: > > This works: if h = c*(e+f*x)^p > > then h/gcd(h,diff(h,x) ) should produce f*x+e. Setting x to 0 > > gives you e. subtracting e from f*x+e and setting x to 1 gives you f. > > > > c is kind of arbitrary, since if c=q^p, you can put it inside the ()^p. > > > > If c is 1, then > > to find p, try log(h)/log(e+f*x). > > > > This all works in Maxima; not sure how if it works in sympy. > > RJF > > > > > > > > On Wednesday, June 8, 2016 at 7:54:05 PM UTC-7, Richard Fateman wrote: > >> > >> I suggest you get rid of all factors not dependent on x by scanning > >> through each term in a product, if you have a product. > >> then you need only find if the expression is R= (e+f*x)^p. > >> compute t A= taylor series expansion around 0 of R and B=taylor series > of > >> diff(R,x). > >> > >> Some algebra should get you e,f,p, if you had some R of that form. > check > >> by substitution. > >> > >> Just a suggestion. > >> > >> RJF > >> > >> > >> > >> On Thursday, May 5, 2016 at 7:01:41 AM UTC-7, Alexander Lindsay wrote: > >>> > >>> I am trying to build a rule for manual integration. I want to test > >>> whether an expression matches the general form: > >>> > >>> c (e + f x)**p > >>> > >>> where c, f, and p can be non-zero expressions not containing x, > whereas > >>> e can be zero but again cannot contain x. > >>> > >>> Moreover, if the expressions matches the above form, I would like to > >>> parse it such that I know the values for c, e, f, and p. > >>> > >>> Any suggestions on general strategies for achieving my goals? I have > >>> been thinking about prolific use of func and args. I imagine that I > >>> would consider various branches for my test since c = 1, e = 0, f = 1, > >>> and p = 1 would all change the class type of the expression or > >>> sub-expressions. > > > > -- > > You received this message because you are subscribed to the Google > Groups > > "sympy" group. > > To unsubscribe from this group and stop receiving emails from it, send > an > > email to [email protected] <javascript:>. > > To post to this group, send email to [email protected] > <javascript:>. > > Visit this group at https://groups.google.com/group/sympy. > > To view this discussion on the web visit > > > https://groups.google.com/d/msgid/sympy/c52fbb2c-a0fc-49f6-b17a-1942797e91fd%40googlegroups.com. > > > > > > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/87048bdb-8e34-4499-8774-1ede542078d0%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
