# [✓] Use the replace rule correctly?

GROUPS:
 Zhonghui Ou 1 Vote I used the replace rule, but it didn't work. Would you like to show how to use the replace rule correctly? In[400]:= eq33 = eq32 /. {A1 -> Sqrt[Dc]*F1* \[Lambda]} Out[400]= \!$$\*SubsuperscriptBox[\(\[Integral]$$, $$0$$, $$T$$]$$\*FractionBox[\( \*SuperscriptBox[\(Dc$$, $$3/2$$]\ \*SuperscriptBox[$$E$$, $$\(- \*FractionBox[ SuperscriptBox[\((lh - x)$$, $$2$$], $$4\ Dc\ t$$]\) + \*FractionBox[$$\(-Dc$$\ t\ \[Theta]c + Dp\ T\ \[Theta]c\), $$Dc - Dp$$]\)]\ F1\ \[Lambda]\), $$\((Dc - Dp)$$\ \*SqrtBox[$$\[Pi]$$]\ \*SqrtBox[$$t$$]\)] \[DifferentialD]t\)\) eq34 = eq33 //. {(Dp*\[Theta]c)/(Dc - Dp) -> A3, (Dc*\[Theta]c)/( Dc - Dp) -> A5, -((lh - x)^2/(4 Dp t)) -> -(A10^2/t), ( Dc^(3/2) F1 \[Lambda])/((Dc - Dp) Sqrt[\[Pi]] ) -> A11} Out[409]= \!$$\*SubsuperscriptBox[\(\[Integral]$$, $$0$$, $$T$$]$$\*FractionBox[\(A11\ \*SuperscriptBox[\(E$$, $$\(- \*FractionBox[ SuperscriptBox[\((lh - x)$$, $$2$$], $$4\ Dc\ t$$]\) + \*FractionBox[$$\(-Dc$$\ t\ \[Theta]c + Dp\ T\ \[Theta]c\), $$Dc - Dp$$]\)]\), SqrtBox[$$t$$]] \[DifferentialD]t\)\) 
 Start with eq1 = (Dc^(3/2) E^(-((lh-x)^2/(4 Dc t))-(-Dc t θc+Dp T θc)/(Dc-Dp)) F1 λ)/(Dc-Dp Sqrt[π] Sqrt[t]) Try your substitutions eq1/.{((Dp θc)/(Dc-Dp))->A3, (Dc θc)/(Dc-Dp)->A5, -(lh-x)^2/(4*Dc*t)->-A10^2/t, Dc^(3/2) F1 λ/((Dc-Dp) Sqrt[π])->A11} Only the A10 substitution succeeds because the other substitutions are within larger expressions. Use Apart to expose the expressions Apart[eq1]/.{((Dp θc)/(Dc-Dp))->A3, (Dc θc)/(Dc-Dp)->A5, -(lh-x)^2/(4*Dc*t)->-A10^2/t, Dc^(3/2) F1 λ/((Dc-Dp) Sqrt[π])->A11} Now the A3, A5 and A10 substitutions succeed. But still the A11 substitution does not succeed because it is inside a larger expression.
 I tried in this way. eq32 = (eq31 /. {t -> (T - t)})*eq30 (A1 Dc E^(-((lh - x)^2/(4 Dc t)) - t \[Theta]c + ( Dp (-t + T) \[Theta]c)/(Dc - Dp)))/((Dc - Dp) Sqrt[\[Pi]] Sqrt[t]) eq33 = eq32 /. {A1 -> Sqrt[Dc] F1 \[Lambda]} /. {(Dp*\[Theta]c)/( Dc - Dp) -> A3} /. {-((lh - x)^2/(4 Dc t)) -> -(A10^2/t)} /. {( Dc^(3/2) F1 \[Lambda])/((Dc - Dp) Sqrt[\[Pi]] ) -> A11} (A11 E^(-(A10^2/t) + A3 (-t + T) - t \[Theta]c))/Sqrt[t] Thanks for your help.Why the Mathematica codes don't display correctly?
 Please show what eqn30 and eqn31 are so that I can understand what you are trying to do.Then please try eq32 = (eq31 /. t -> (T - t))*eq30 eq33 = eq32 /. A1->Sqrt[Dc] F1 \[Lambda] eqn34 = eqn33 /. (Dp*\[Theta]c)/(Dc-Dp)->A3 eqn35 = eqn34 /. -((lh-x)^2/(4 Dc t)) -> -(A10^2/t) eqn36 = eqn35 /. (Dc^(3/2) F1 \[Lambda])/((Dc-Dp) Sqrt[\[Pi]] )->A11 and paste all the results so we can see each substitution separately and try to understand where it is not working