Re: Simplification During Integration

*To*: mathgroup at smc.vnet.net*Subject*: [mg21472] Re: [mg21391] Simplification During Integration*From*: "Allan Hayes" <hay at haystack.demon.co.uk>*Date*: Tue, 11 Jan 2000 04:17:51 -0500 (EST)*References*: <84s751$q6r@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Andrzej: With Integrate[Factor[y], t] Sin[g]^2*(2*t*Cos[g/2]^3*Sec[g]*Sin[g/2] - Cos[g/2]*Sec[g]*Sin[g/2]^3*Sin[2*t])*Tan[g]^2 we still have some changes. But we can use Integrate[y /. p : _[g] :> A[p], t] /. A[p_] -> p (1*Sin[g]^2*Sin[2*t]*(Sin[g] - Tan[g])*Tan[g]^2)/4 + (1*t*Sin[g]^2*Tan[g]^2*(Sin[g] + Tan[g]))/2 Allan --------------------- Allan Hayes Mathematica Training and Consulting Leicester UK www.haystack.demon.co.uk hay at haystack.demon.co.uk Voice: +44 (0)116 271 4198 Fax: +44 (0)870 164 0565 "Andrzej Kozlowski" <andrzej at tuins.ac.jp> wrote in message news:84s751$q6r at smc.vnet.net... > This happen only in rather special cases, usually involving triginometric > functions. If you prefer you can make Mathematica factor out the common > terms, e.g. : > > In[14]:= > Integrate[Factor[y], t] > Out[14]= > 2 g 3 g > Sin[g] (2 t Cos[-] Sec[g] Sin[-] - > 2 2 > > g g 3 2 > Cos[-] Sec[g] Sin[-] Sin[2 t]) Tan[g] > 2 2 > > You can't however in general stop Mathematica transforming the remaining > terms (even those that do not depend on the variable of integration) since > it is often the case that one can reduce an integral to a form that can be > integrated only by performing such transformations. > > > > From: Joel Storch <jstorch at earthlink.net> To: mathgroup at smc.vnet.net > > Organization: EarthLink Network, Inc. > > Date: Mon, 3 Jan 2000 03:12:24 -0500 (EST) > > To: mathgroup at smc.vnet.net > > Subject: [mg21472] [mg21391] Simplification During Integration > > > > In performing a definite or indefinite integral, Mathematica performs > > transformations on parameters which are not dependent upon the variable > > of integration. How do I supress this type of behavior ? > > > > Example: Consider the two term expression > > > > y=Tan[g]^2 Sin[g]^3 Cos[t]^2 + Tan[g]^3 Sin[g]^2 Sin[t]^2 > > > > Integrate[y,{t,0,a}] results in an expression in which the > > trigonometric functions of g have been transformed. I would > > expect Mathematica to recognize that these factors are independent of t > > and simply "pull them out" from the integral. Integrating either of the > > terms separately, does not result in these type of transformations. > > > >