#define _USE_MATH_DEFINES
#include <iostream>
#include <cmath>

using namespace std;

double GetY(double x)
{
    //log() - взять натуральный логорифм
    //pow(x,y) возвести x в y степень
    return log(pow(M_E, x)) + 1;
    //return 5;
}

struct Prym
{
    public:

        double x1, x2, y;
        double Square()
        {
            return (x2 - x1) * y;
        };

        double GetX2() { return x2; }

        Prym() { x1 = 0; x2 = 0; y = 0; }

        Prym(double x1, double x2, double y)
        {
            this->x1 = x1;
            this->x2 = x2;
            this->y = y;
        }
};

double GetStep(double x)
{
    const float accuracy = 0.001f;
    double step = 0;

    while (true)
    {
        step += 0.001;
        //cout << step << endl;
        if(abs( GetY(x) - GetY(x + step) ) < accuracy)
        {
            break;
        }
    }

    return step;
}

int main()
{
    setlocale(LC_ALL, "rus");

    const float a = 0, b = 1;
    double step;

    double sum;
    double x = a;
    step = GetStep(x);
    Prym pr1 = Prym(x, x + step, GetY(x));
    sum = pr1.Square();
    x += step;
    Prym pr2;

    while (true)
    {
        step = GetStep(x);
        if (x + step <= b)
        {
            x += step;
            pr2 = Prym(pr1.GetX2(), x, GetY(x));
            sum += pr2.Square();
            //cout << sum << endl;
            pr1 = pr2;
        }
        else
            break;
    }

    cout << "Интеграл равен: " << sum;
}