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


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


/* [wxMaxima: comment start ]
Priklad 2.8.
   [wxMaxima: comment end   ] */


/* [wxMaxima: input   start ] */
zadani:'integrate(x^2*(4*x^3-5)^7,x);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
changevar(zadani,4*x^3-5=t,t,x);
/* [wxMaxima: input   end   ] */


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


/* [wxMaxima: input   start ] */
subst(4*x^3-5,t,%);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Priklad 2.9.
   [wxMaxima: comment end   ] */


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


/* [wxMaxima: input   start ] */
sub:changevar(zadani,acos(x)=t,t,x);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
expr1:part(part(sub,1),1);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
expr2:subst([denom(expr1)=sin(t),acos(cos(t))=t],expr1);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
int:(-1)*integrate(expr2,t);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
subst(acos(x),t,int);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Priklad 2.10.
   [wxMaxima: comment end   ] */


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


/* [wxMaxima: input   start ] */
sub:changevar(zadani,x=sin(t),t,x);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
subst(1-sin(t)^2,num(part(sub,1)),part(sub,1));
/* [wxMaxima: input   end   ] */


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


/* [wxMaxima: input   start ] */
integrate(%,t);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
subst(solve(x=sin(t),t),t,%);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: comment start ]
Priklad 2.11.
   [wxMaxima: comment end   ] */


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


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


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


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


/* [wxMaxima: input   start ] */
subst(sol[3],t,vysl);
/* [wxMaxima: input   end   ] */



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