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

> 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);

> IT12:=changevar(t=tan(x), (IT12, t),x);

10-misol. bu integralni topishda yuqoridagilardan farqli quyidagicha almashtrish qilamiz:

Bu holda
=
1) o`zgaruvchini almashtirish yordamida integralni topish.
> restart;
> with(student):
> IT13:=changevar(2+3*sin(2*x)=t,
int(cos(2*x)/(2+3*sin(2*x))^(2/3),x),t);

> IT13:=changevar(t=2+3*sin(2*x), (IT13, t),x);

2) Bevosita integrallash.
> restart;
> Int(cos(2*x)/(2+3*sin(2*x))^(2/3),x)=
int(cos(2*x)/(2+3*sin(2*x))^(2/3),x);

3. Sinus va kosinus toq darajali bo`ganda integrallash


a)
bu yerda t=cosx.
b)
bu yerda t=sinx.
> restart;
> IT3m:=Int(sin(x)^(2*m+1),x)=int(sin(x)^(2*m+1),x);

> m:=1:IT3m;
> m:=2:IT3m;

11-misol.. integralni hisoblang.
YEchish. va ekanligini hamda
almashtirish kiritib, quyidagini hosil hilamiz:

> restart;
> IT5m:=Int(sin(x)^3*cos(x)^4,x)=int(sin(x)^3*cos(x)^4,x);