// 10/4/1
// E = 0.001
// f1 = 1 + 4 / (x^2+ 1)
// f2 = x^3
// f3 = 2^(−x)

#include <stdio.h>
#include <stdlib.h>
#include <math.h>


double eps = 0.001;
double  eps1 = 0.0001;
double  eps2 = 0.0001;


double f1(double x)
{
    return 1 + 4 / (x * x + 1);
    //return 1/x;
}

double f1_1(double x)
{
    return - 8 * x / ((x * x + 1) * (x * x + 1));
    //return -1/(x*x);
}

double f1_2(double x)
{
    return 32 * powf(x, 2) / (powf((powf(x, 2) + 1), 3)) - 8 / (powf((x * x + 1), 2));
}




double f2(double x)
{
    return x * x * x;
}

double f2_1(double x)
{
    return 3 * x * x;
}

double f2_2(double x)
{
    return 6 * x;
}




double f3(double x)
{
    return pow(2, (-x));
}

double f3_1(double x)
{
    return -log(2) * pow(2, (-x));
}

double f3_2(double x)
{
    return log(2) * log(2) * pow(2, (-x));
}



double root(double (*f)(double), double (*g)(double), double (*f1)(double), double (*g1)(double), double a, double b, double eps1)
{
    double a1 = 0, b1 = 0;
    while (fabs(a - b) > eps1)
    {
        if (((f(a) - g(a)) < 0) && ((f((a + b) / 2) - g((a + b) / 2)) > ((f(a) - g(a) + f(b) - g(b)) / 2)))
        {
        a1 = a - (b - a) * (f(a) - g(a)) / (f(b) - g(b) - f(a) + g(a));
        b1 = b - (f(b) - g(b)) / (f1(b) - g1(b));

        a = a1;
        b = b1;
        }
        else
        {
        b1 = b - (a - b) * (f(b) - g(b)) / (f(a) - g(a) - f(b) + g(b));
        a1 = a - (f(a) - g(a)) / (f1(a) - g1(a));

        a = a1;
        b = b1;
        }
    }
    return b;
}



double integral(double (*f)(double), double a, double b, double eps2)
{
    double res = 100, h, n = 20, In = 0, I2n = 10;
    h = (b - a) / n;
    for (int i = 0; i < n; i++)
    {
        res += f(a + (i + 0.5) * h);
    }
    res *= h;
    In = res;
    n *= 2;

    h = (b - a) / n;
    for (int i = 0; i < n; i++)
    {
        res += f(a + (i + 0.5) * h);
    }
    res *= h;
    I2n = res;

    double p = 1/3;

    while (p * fabs(In - I2n) > eps2)
    {
        In = I2n;
        n *= 2;
        res = 0;
        h = (b - a) / n;
        for (int i = 0; i < n; i++)
        {
            res += f(a + (i + 0.5) * h);
        }
        res *= h;
        n *= 2;
        I2n = res;
    }
    return I2n;
}



int main(void)
{
    double a = -10, b = 10;
    double x_1_2 = root(f1, f2, f1_1, f2_1, a, b, eps1);

    a = -10;
    b = 10;
    double x_2_3 = root(f2, f3, f2_1, f3_1, a, b, eps1);

    a = -10;
    b = -0.5;
    double x_1_3 = root(f1, f3, f1_1, f3_1, a, b, eps1);

    printf("%lf    %lf    %lf\n", x_1_2, x_2_3, x_1_3);

    double res = 0, first, sec, third;
    first = integral(f1, x_1_3, x_1_2, eps2);
    sec = integral(f3, x_1_3, x_2_3, eps2);
    third = integral(f2, x_2_3, x_1_2, eps2);

    res = first - sec - third;

    printf("%lf\n", res);

    return 0;
}