高斯-勒让德公式 求积分

#include <iostream>
#include <cmath>
using namespace std;
//计算f(x)=1/x 在[1,3]上的积分 

double f(double x){
    return 1.0/(x+2);
}

double f1(double x){
    return 1.0/(x+5);
}
double f2(double x){
    return 1.0/(x+7); 
}

double f3(double x){
    return 1.0/(x+9);
}
double f4(double x){
    return 1.0/(x+11); 
}

int main(){
    //运用三点高斯公式积分值 
    printf("%2.8f
",    (0.5555556*f( -0.7745967)+0.8888889*f( 0 )+0.5555556*f( 0.7745967) ));

    //运用五点高斯公式求积分值 
    printf("%2.8f
",  0.2369269*f(-0.9061799)+ 0.2369269*f(0.9061799)+0.4786287*f(-0.5384693)+0.4786287*f(0.5384693) +
    0.5688889*f(0) );
    printf("
");
    
    //将区间4等分，分别利用二点高斯公式，然后累加得积分值 
        printf("%2.8f
",f1( -1.0/sqrt(3.0))+f1(1.0/sqrt(3.0))  );
        printf("%2.8f
",f2( -1.0/sqrt(3.0))+f2(1.0/sqrt(3.0))  );    
        printf("%2.8f
",f3( -1.0/sqrt(3.0))+f3(1.0/sqrt(3.0))  );
        printf("%2.8f
",f4( -1.0/sqrt(3.0))+f4(1.0/sqrt(3.0))  );
            
        printf("sum=%2.8f
",f1( -1.0/sqrt(3.0))+f1(1.0/sqrt(3.0)) +f2( -1.0/sqrt(3.0))+f2(1.0/sqrt(3.0)) +f3( -1.0/sqrt(3.0))+f3(1.0/sqrt(3.0)) +f4( -1.0/sqrt(3.0))+f4(1.0/sqrt(3.0))  );
            
}