> m:=3:value(Ik2);
> m:=4:Ik2:=value(Ik2);
> m:=4:a:=1:Ik2:=value(Ik2);
n=2,3 bo`lganda integralini formula asosida topish.
1) > restart;
> Ik3:=int((A*(t-p/2)+B)/(t^2+a^2)^m,t);
hosil bolgan tenglikning chap va o`ng ko`phadlarining darajalari bo`icha mos koeffitsientlarni tenglashtirib quyidagi sistemani tuzamiz:
Sodda kasirlarning koeffitsientlarni topish va integrallash:
> restart;
> f:=x->(1-x^3)/(x^5+x^2);
> y1:=x->A1/x+A2/x^2+A3/(x+1)+(A4*x+A5)/(x^2-x+1);
> p:=simplify(y1(x));
> pol1:=f(x)*(x^5+x^2); pol2:=p*x^2*(x+1)*(x^2-x+1);
> kp0:=coeff(pol1,x,0)=coeff(pol2,x,0);
> kp1:=coeff(pol1,x,1)=coeff(pol2,x,1);
> kp2:=coeff(pol1,x,2)=coeff(pol2,x,2);
> kp3:=coeff(pol1,x,3)=coeff(pol2,x,3);
> kp4:=coeff(pol1,x,4)=coeff(pol2,x,4);
> k:=solve({kp0,kp1,kp2,kp3,kp4},{A1,A2,A3,A4,A5});
> A1:=0; A4:=-2/3; A3:=2/3; A5:=-2/3; A2:=1;y1(x);
> int(y1(x),x);
Topilgan koeffitsientlar asosida berilgan kasirni sodda kasirlarga ajratilgan ko`rinishin yozamiz:
Bebosita sodda kasirlarga ajratish:
> factor(x^5+x^2);
> with(genfunc): rgf_pfrac((x^6+1)/(x^5+x^2), x);
> Int((x^6+1)/(x^5+x^2), x)=int((x^6+1)/(x^5+x^2),x);
Ba`zi bir trigonometrik ifodalarni integrallash
1. integralda R o`z argumentlarining ratsional funksiyasi bo`lsin. U holda, bu integralda umumiy trigonometrik almashtirish deb ataluvchi
almashtirish yordamida ratsional funksiya integraliga kelinadi. Haqiqatdan ham,
ekanligini e`tiborga olsak,
,
bu yerda - ratsional funksiya.
1-misol. Bu almashtirish yordamida integrallar jadvalidagi 16-formulani keltirib chiqarish mumkin:
17-formula esa ekanligidan va 16-formuladan kelib chiqadi.
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