Re: Help needed - Mathematica code

*To*: mathgroup at smc.vnet.net*Subject*: [mg123026] Re: Help needed - Mathematica code*From*: Barrie Stokes <Barrie.Stokes at newcastle.edu.au>*Date*: Mon, 21 Nov 2011 04:26:01 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201111181122.GAA06449@smc.vnet.net>

Daniel's (successful) integration is of x*y[x], whereas I read the original posting as wanting the integration of x*y[x]^b, in which case Integrate[ x*y[x]^b, {x, 0, a}, Assumptions -> {a > 0, 1 > b > 0, c > 0, d > 0} ] produces the (slightly simpler and unconditional on b) output (a ((-1 + c)^(1/b))^b d)/c Barrie >>> On 18/11/2011 at 10:22 pm, in message <201111181122.GAA06449 at smc.vnet.net>, Daniel Lichtblau <danl at wolfram.com> wrote: > > ----- Original Message ----- >> From: "Tetsu Tetsu.HDD" <tetsu.hdd at gmail.com> >> To: mathgroup at smc.vnet.net >> Sent: Thursday, November 17, 2011 5:04:08 AM >> Subject: Help needed - Mathematica code >> >> Hi, >> >> I would greatly appreciate if anyone can help me out of this problem. >> >> To explain my problem, I will use LaTeX code. >> >> Given a>0, 1>b>0, c>0 and d>0, I want to calculate the following >> >> \int_0^a X Y(X)^b dX >> >> where Y(X) is defined by >> >> (c - \frac{Y}{d-X Y^b}) X Y^{b-1}=1 >> >> Can you tell me Mathematica codes for this problem? >> >> Thank you in advance. >> >> T > > If I understand correctly, then it might be that you want something along > the lines below. > > In[164]:= > y[x_] := y /. First[Solve[c - (y/(d - x*y^b))*x*y^(b - 1) == 1, y]] > > In[166]:= Integrate[x*y[x], {x, 0, a}, > Assumptions -> {a > 0, 1 > b > 0, c > 0, d > 0}] > > During evaluation of In[166]:= Solve::ifun:Inverse functions are being used > by Solve, so some solutions may not be found; use Reduce for complete > solution information. >> > > Out[166]= ConditionalExpression[(a^2* > b*((-1 + c)/a)^(1/b)*(d/c)^(1/b))/(-1 + 2*b), b > 1/2] > > Daniel Lichtblau > Wolfram Research >

**References**:**Re: Help needed - Mathematica code***From:*Daniel Lichtblau <danl@wolfram.com>