%龍貝格加速算法(課本71頁表2-5)應用于習題2_14
function r=longbeige(a,b,n,e)


t=[];
s=[];
r=[];
result=[];
h=b-a;
% if a==0
%     v=1;
% else
%     v=f(a);
% end

t1=h/2*(f(a)+f(b));
t(1)=t1
for k=1:n
    k
    s=0;
    x=a+h/2;
    while x<b
        s=s+f(x);
        x=x+h;
    end
    t2=t1/2+h/2*s;
    s2=t2+(t2-t1)/3;
    t(k+1)=t2
    si(k)=s2
    if k==1
        h=h/2;
        t1=t2;
        s1=s2;
    else
        c2=s2+(s2-s1)/15;
        c(k-1)=c2
        if k==2
            c1=c2;
            h=h/2;
            t1=t2;
            s1=s2;
            else
                r2=c2+(c2-c1)/63;
                r(k-2)=r2
                if k==3
                    r1=r2;
                    c1=c2;
                    h=h/2;
                    t1=t2;
                    s1=s2;
                else
                    if abs(r2-r1)<e
                        r=r2;
                        break
                    else
                        r1=r2;
                        c1=c2;
                        h=h/2;
                        t1=t2;
                        s1=s2;
                        
                    end
                end
            end
        end
    end
    if k==n
    '加速不夠，請增加加速次數'
    end
    t=t';
    si=[0 si];
    si=si';
    c=[0 0 c];
    c=c';
    r=[0 0 0 r];
    r=r';
    k=[0 1 2 3 4 5];
    k=k';
    result=[k t si c r]
    
        
       
            
                
    




function y=f(x)
y=(x^2+x+1)*cos(x);