1
$\begingroup$

As shown in the following program, the q[t] in a can be collected from the integration by defining the integration of fe1[x] as Infe1[x], the same is true for fe2[x] in b. But for the equation c, how can I collect q[t] from it?

fe1 /: Integrate[fe1[x_], x_] := Infe1[x];
fe2 /: Integrate[fe2[x_], x_] := Infe2[x];

a = Integrate[fe1[x]*q[t], {x, 0, L1}]

b = Integrate[fe2[x]*q[t], {x, 0, L1}]   

c = Integrate[fe1[x]*fe2[x]*q[t], {x, 0, L1}]
Improve this question
$\endgroup$
1
  • $\begingroup$ @SunnySky, if you want to convert typeset math (TraditionalForm) input into InputForm you can use Hold[ yourexpression ] // InputForm and copy and paste the bit inside Hold[]. $\endgroup$
    – Verbeia
    Commented Aug 29, 2012 at 3:59

1 Answer 1

Reset to default
2
$\begingroup$

You could do it with a rule:

myrule = Integrate[Times[x_, q[t]], y_] :> q[t] Integrate[x, y]

c = Integrate[fe1[x]*fe2[x]*q[t], {x, 0, L1}] /. myrule

(*  ==>  Integrate[fe1[x]*fe2[x], {x, 0, L1}]*q[t]   *)

Edit:

For more generality, you could do

myrule2 = Integrate[Times[x_, c_], {y_, y1_, y2_}] /; FreeQ[c, y] :> c  Integrate[x, {y, y1, y2}];

Integrate[(1 + Exp[h[t]]^2) g[x, t] f[x] Exp[q[t]], {x, 0, L1}] //. myrule2

(* ==> E^q[t]*(1 + E^(2*h[t])) * Integrate[f[x]*g[x, t], {x, 0, L1}] *)

Note the use of ReplaceRepeated (//.) rather than just ReplaceAll (/.).

Improve this answer
$\endgroup$
4
  • $\begingroup$ your answer works well. thank you very much. Moreover, If the q[t] is substituted by q[t]*g[t]*r[t] or even a more complex functions that depend on "t", then how can I collect them from the integration without defining rules for each special functions? $\endgroup$
    – SunnySky
    Commented Aug 29, 2012 at 7:12
  • $\begingroup$ @SunnySky please see if the update helps you $\endgroup$
    – ecoxlinux
    Commented Aug 29, 2012 at 14:26
  • $\begingroup$ yes, your answer is very good. may be "//. myrule" should be replaced by "//. myrule2". Thank you very much. $\endgroup$
    – SunnySky
    Commented Aug 30, 2012 at 1:57
  • $\begingroup$ Indeed. Corrected. $\endgroup$
    – ecoxlinux
    Commented Aug 30, 2012 at 2:45

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.