#include "stdio.h"
#include "math.h"


double fsimpf(x) /*要進行計算的被積函數(shù)*/
double x;
{ 
	double y;
    y=log(1.0+x)/(1.0+x*x);
    return(y);
}

double fsimp(a,b,eps) /*辛普森算法*/
double a,b,eps; /*a為積分下限，b為積分上限，eps是希望達到的精度*/
{ 
    int n,k;
    double h,t1,t2,s1,s2,ep,p,x;
    n=1; h=b-a;
    t1=h*(fsimpf(a)+fsimpf(b))/2.0;  /*用梯形公式求出一個大概的估值*/
    s1=t1;
    ep=eps+1.0;
    while (ep>=eps)
	{  
		/*用梯形法則計算*/
		p=0.0;
		for (k=0;k<=n-1;k++)
		{ 
			x=a+(k+0.5)*h;
			p=p+fsimpf(x);
		}
		t2=(t1+h*p)/2.0;
		/*用辛普森公式求精*/
		s2=(4.0*t2-t1)/3.0;
		ep=fabs(s2-s1);
		t1=t2; s1=s2; n=n+n; h=h/2.0;
	}
    return(s2);
}
main()
{ 
	double a,b,eps,t;
    a=0.0; b=1.0; eps=0.0000001;
    t=fsimp(a,b,eps);
    printf("\n");
    printf("t=%e\n",t);
    printf("\n");
}