code: import static java.lang.Math.*;
  import java.util.function.Function;
  
  public class Test {
      final static int N = 5;
  
      static double[] lroots = new double[N];
      static double[] weight = new double[N];
      static double[][] lcoef = new double[N + 1][N + 1];
  
      static void legeCoef() {
          lcoef[0][0] = lcoef[1][1] = 1;
  
          for (int n = 2; n <= N; n++) {
  
              lcoef[n][0] = -(n - 1) * lcoef[n - 2][0] / n;
  
              for (int i = 1; i <= n; i++) {
                  lcoef[n][i] = ((2 * n - 1) * lcoef[n - 1][i - 1]
                          - (n - 1) * lcoef[n - 2][i]) / n;
              }
          }
      }
  
      static double legeEval(int n, double x) {
          double s = lcoef[n][n];
          for (int i = n; i > 0; i--)
              s = s * x + lcoef[n][i - 1];
          return s;
      }
  
      static double legeDiff(int n, double x) {
          return n * (x * legeEval(n, x) - legeEval(n - 1, x)) / (x * x - 1);
      }
  
      static void legeRoots() {
          double x, x1;
          for (int i = 1; i <= N; i++) {
              x = cos(PI * (i - 0.25) / (N + 0.5));
              do {
                  x1 = x;
                  x -= legeEval(N, x) / legeDiff(N, x);
              } while (x != x1);
  
              lroots[i - 1] = x;
  
              x1 = legeDiff(N, x);
              weight[i - 1] = 2 / ((1 - x * x) * x1 * x1);
          }
      }
  
      static double legeInte(Function<Double, Double> f, double a, double b) {
          double c1 = (b - a) / 2, c2 = (b + a) / 2, sum = 0;
          for (int i = 0; i < N; i++)
              sum += weight[i] * f.apply(c1 * lroots[i] + c2);
          return c1 * sum;
      }
  
      public static void main(String[] args) {
          legeCoef();
          legeRoots();
  
          System.out.print("Roots: ");
          for (int i = 0; i < N; i++)
              System.out.printf(" %f", lroots[i]);
  
          System.out.print("\nWeight:");
          for (int i = 0; i < N; i++)
              System.out.printf(" %f", weight[i]);
  
          System.out.printf("%nintegrating Exp(x) over [-3, 3]:%n\t%10.8f,%n"
                  + "compared to actual%n\t%10.8f%n",
                  legeInte(x -> exp(x), -3, 3), exp(3) - exp(-3));
      }
  }
  