#include <stdio.h>
#include <math.h>
 
float f(float);
float a;
float b;
float x;
float h;
float sum;
int n;
int j;
 
float first;
float second;
int main() {
  a = 0;
  b = 2;
  n = 8;
  h = (b - a) / n;
 
  sum = (h / 3) * (f(a) + f(b));
 
  printf("%f\n", sum);
 
  for (j = 1; j <= ((n / 2.0f) - 1); j++) {
    first = first + (2.0f / 3.0f) * h * f(a + (2 * j * h));
  }
  printf("first sum: %f\n",first);
 
  for (j = 1; j <= (n / 2.0f); j++) {
    second = second + (4.0f / 3.0f) * h * f(a + ((2 * j - 1) * h));
  }
  printf("second sum: %f\n",second );
 
  sum = sum + first + second;
  printf("The value of the integral is: %f\n", sum); 
  return 0;
}
 
float f(float x) {
  float value;
  value = x * x * (log(x * x + 1));
  return value;
}