Re: Help needed - Mathematica code

*To*: mathgroup at smc.vnet.net*Subject*: [mg122948] Re: Help needed - Mathematica code*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Fri, 18 Nov 2011 06:22:21 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

----- 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

**Follow-Ups**:**Re: Help needed - Mathematica code***From:*Barrie Stokes <Barrie.Stokes@newcastle.edu.au>