/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created with wxMaxima version 17.10.1 ] */
/* [wxMaxima: title   start ]
Priklady - kapitola 2 - e
   [wxMaxima: title   end   ] */


/* [wxMaxima: comment start ]
Cisla prikladu koresponduji s diplomovou praci
   [wxMaxima: comment end   ] */


/* [wxMaxima: comment start ]
Priklad 2.22.
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
zadani:'integrate(sqrt(x^2+4*x-5),x);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
sub1:changevar(zadani,t=x+2,t,x);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
sub2:subst(sqrt(t^2-9),sqrt(t-3)*sqrt(t+3),sub1);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
t:3/sin(u)$ dert:diff(t,u);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
int:'integrate(dert*sqrt(t^2-9),u);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
assume(sin(u)>0)$ int2:factor(int);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
assume(v>0)$ changevar(int2,v=cos(u),v,u);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
iresult:expand(ev(%,nouns));
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
sub3:subst(cos(u),v,iresult);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
sub4:subst(sqrt(1-(9/'t^2)),cos(u),sub3);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
sub5:subst(x+2,'t,sub4);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
expand(radcan(sub5));
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
forget(sin(u)>0);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
forget(v>0);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Priklad 2.23.
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
zadani:'integrate((1/(sqrt(x)*(x^(1/3)+1)^2)),x);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
assume(t>0)$ sub:changevar(zadani,x=t^6,t,x);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
expr:part(part(sub,2),1);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
partfrac(expr,t);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
batch("C:/Users/procedura-rekurent-t");
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
int:K(1)-K(2);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
result:expand(6*int);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
subst(x^(1/6),t,result);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
forget(t>0);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Priklad 2.24.
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
zadani:'integrate((x^3/(sqrt((1-x^2)^3))),x);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
assume(t>0)$ changevar(zadani,t^2=1-x^2,t,x);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
ev(%,nouns);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
result:subst(sqrt(1-x^2),t,%);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
ratsimp(result);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
forget(t>0);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Priklad 2.25.
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
zadani:'integrate(1/(x^2*((x^3+2)^5)^(1/3)),x);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
sol:solve(t^3=2*x^(-3)+1,x);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
changevar(zadani,sol[3],t,x);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
ev(%,nouns);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
factor(subst((2*x^(-3)+1)^(1/3),t,%));
/* [wxMaxima: input   end   ] */



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