Trigonometrik funksiyalar qatnashgan ifodalarni integrallash

> restart;
> with(student):
> IT9:=changevar(tan(x)=t,Int(1/(sin(x)^2-
4*sin(x)*cos(x)+ 5*cos(x)^2),x),t);

> IT9:=value(%);
> IT9:=changevar(t=tan(x), (IT9, t),x);

2) Bevosita integrallash.
> restart;
> Int(1/(sin(x)^2-4*sin(x)*cos(x)+5*cos(x)^2),x)= int(1/(sin(x)^2-4*sin(x)*cos(x)+5*cos(x)^2),x);

5. , R –ratsional funksiya. umumiy almashtirishdan foydalanish mumkin. Ammo qulayroq bo`lgan

almashtirishdan foydalansak,

ga kelamiz, bu yerda - ratsional funksiya.
7-misol. | |=
= =
=|t=tgx|=
1) o`zgaruvchini tgx=t almashtirish yordamida integralni topish.
> restart;
> with(student):
> IT7:=changevar(tan(x)=t,Int(1/(tan(x)+1),x),t);

> IT7:=value(%);
> IT7:=changevar(t=tan(x), (IT7, t),x);

2) Bevosita integrallash.
> restart;
> Int(1/(tan(x)+1),x)=int(1/(tan(x)+1),x);
8-misol. | |=
= =|t=tgx|=
1) o`zgaruvchini tgx=t almashtirish yordamida integralni topish.
> restart;
> with(student):
> IT10:=changevar(tan(x)=t,Int(tan(x)^3,x),t);

> IT10:=value(%);
> IT10:=changevar(t=tan(x), (IT10, t),x);

2) Bevosita integrallash.
> restart;
> Int(tan(x)^3,x)=int(tan(x)^3,x);

9-misol. tgx=t almashtirish yordamida integralni topish
> restart;
> with(student):
> IT12:=changevar(tan(x)=t,int(tan(x)^5,x),t);