x1, x2 = 3, 6


def fx(x):
    return x/(4+x**2)

# n等分，x1到x2的区间，type=1表示梯形法，type=2表示辛普森法
def CompositeNewtonCotes(n, type):
    if type == 1:
        h = (x2 - x1) / n
        result = 0
        for i in range(n):
            result += (fx(x1 + i * h) + fx(x1 + (i + 1) * h))
        result *= (h / 2)
        return result
    elif type == 2:
        h = (x2 - x1) / n
        result = -fx(x1) + fx(x2)
        for i in range(n):
            result += (4 * fx(x1 + (i + 0.5) * h) + 2 * fx(x1 + i * h))
        result *= (h / 6)
        return result
    

if __name__ == "__main__":
    print("Composite Trapezoidal Rule: ", CompositeNewtonCotes(8, 1))
    print("Composite Simpson's Rule: ", CompositeNewtonCotes(4, 2))