Ratsional funksiyani (kasrni) integrallash. Ba`zi bir trigonometrik ifodalarni integrallash

> IT8:=changevar(t=tan(x), (IT8, t),x);

2) Bevosita integrallash.
> restart;
> Int(1/(1+cos(x)^2),x)=int(1/(1+cos(x)^2),x);

6-misol. da sinx va cosx larga nisbatan juft funktsiya bo`lgani uchun integralni tgx=t almashtirish yordamida topamiz.

Ekanini etiborga olib,
=
=
1) o`zgaruvchini tgx=t almashtirish yordamida integralni topish.
> 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.