#include <iostream>
#include <cmath>
#include <iomanip>

using namespace std;
// s = 3.059116539645953


double F(double x)
{
    return pow(M_E, x) / x; // функция
}


double riemann_sum(double a, double b, int n) //прямоугольник
{
    double s = 0, h, x;
    h = (b - a) / n;

    for (int i = 0; i < n; i++)
    {
        x = a + i * h;
        s += F(x + h/2);
    }

    s *= h;
    //s += ((h * h) / 24) * 1.84726; // R1 считай сам
    return s;
}


double trapezoidal_rule(double a, double b, int n) //трапеция
{
    double s = 0, x1, x2, h;
    h = (b - a) / n;

    for (int i = 0; i < n; i++)
    {
        x1 = a + i * h;
        x2 = x1 + h;
        s += F(x1) + F(x2);
    }
    s *= h / 2;
    //s -= ((h * h) / 12) * 1.84726; // R2 считай сам
    return s;
}


double simpsons_rule(double a, double b, int n) // парабола
{
    double s = 0, x1, x2, x3, h;
    h = (b - a) / n;

    for (int i = 0; i < n / 2; i++)
    {
        x1 = a + 2 * i * h;
        x2 = x1 + h;
        x3 = x2 + h;
        s += F(x1) + 4 * F(x2) + F(x3);
    }
    s *= h / 3;
    //s -= ((h * h * h * h) / 180) * 6.36019; // R3 считай сам
    return s;
}

double runge_rule_difference(double (*method)(double, double, int), int n)
{
    double I1, I2;

    I1 = (*method)(1, 2, n);
    I2 = (*method)(1, 2, n * 2);

    return fabs(I2 - I1);
}


int main() {
    double s_riemann, s_trapezoidal, s_simpson, e;

    e = 0.0000001;


    cout << "The program calculates the integration e ^ x / x on the spider [1;2]" << endl
         << "Input e " ;
    //cin >> e;
    cout << endl;

    int n = 1;
    while (e < runge_rule_difference(riemann_sum, n) / 3) { n *= 2; }
    s_riemann = riemann_sum(1, 2 , n * 2);

    cout << "Result for the rectangle method " << s_riemann << endl
         << "n = " << n * 2 << endl
         << "Runge rule "<< runge_rule_difference(riemann_sum, n) / 3 << endl << endl;

    n = 1;
    while (e < runge_rule_difference(trapezoidal_rule, n) / 3) { n *= 2; }
    s_trapezoidal = trapezoidal_rule(1, 2 , n * 2);

    cout << "Result for the trapezoid method " << s_trapezoidal << endl
         << "n = " << n * 2 << endl
         <<"Runge rule " << runge_rule_difference(trapezoidal_rule, n) / 3 <<  endl << endl;

    n = 1;

    while (e < runge_rule_difference(simpsons_rule, n) / 15) { n *= 2; }

    s_simpson = simpsons_rule(1, 2 , n * 2);

    cout << "Result for Simpson formula " << s_simpson << endl
         << "n = " << n * 2 << endl
         << "Runge rule " << runge_rule_difference(simpsons_rule, n) / 15 <<  endl << endl;


    return 0;
}