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- "Continuous antiderivatives and change of variable in integrals"
-
- "Author: Valeriu Anisiu, anisiu@math.ubbcluj.ro"
- "address: Faculty of Mathematics and Computer Science"
- " Babes-Bolyai University"
- " Kogalniceanu 1 Street"
- " 3400 Cluj-Napoca, Romania"
-
- MAKECONT(u,x,v,a):=LOOP(IF(v=[],RETURN(u)),a:=FIRST(v),u:=u+STEP(x-a)*(LIM(u,~
- x,a,-1)-LIM(u,x,a,1)),v:=REST(v))
-
- CONT_INT(u,x,v,a:="_",b,w):=PROG(w:=MAKECONT(INT(u,x),x,v),IF(a="_",RETURN(w)~
- ),LIM(w,x,b)-LIM(w,x,a))
-
- INTSUBST(y,varx,rx,t_,rt:="_",x,w,ux,ut):=PROG(IF(NOT(VECTOR?(varx)),varx:=[v~
- arx]),x:=FIRST(varx),IF(RHS(rx)="euler1",PROG(w:=LHS(rx),rx:=SQRT(w)=SQRT(LIM~
- (w/x^2,x,inf))*x+t_,rt:=rx^2)),IF(RHS(rx)="euler2",PROG(w:=LHS(rx),rx:=SQRT(w~
- )=SQRT(LIM(w,x,0))+x*t_,rt:=rx^2/x)),IF(RHS(rx)="euler3",PROG(w:=FACTORS(LHS(~
- rx),Complex,x),rx:=SQRT(LIM(LHS(rx)/x^2,x,inf)*w SUB 1 SUB 1/w SUB 2 SUB 1)=t~
- _,rt:=rx^2)),IF(RHS(rx)=0,rx:=rx=t_),IF(rt="_",rt:=rx),ut:=FIRST(RHS(SOLVE([r~
- t],x))),w:=STRING(ut),IF(w SUB 1="IF",ut:=w SUB (-1)),ux:=RHS(SOLVE(rx,t_)),I~
- F(DIF(ux,x)=0 OR DIF(ut,t_)=0,RETURN("inapplicable")),w:=INT(SUBST(y,LHS(rx),~
- RHS(rx),x,ut)*DIF(ut,t_),t_),w:=LIM(w,t_,ux),IF(DIM(varx)=1,w,LIM(w,x,varx SU~
- B 3)-LIM(w,x,varx SUB 2)))
-
-