import math

def f(x):
    if x == 0:
        return 0
    else:
        a = (math.pow(x, 2) + 1) * math.pow(math.sin(x), 3) / (x * math.log(1 + x))
        b = (1 + math.pow(x, 2)) * math.pow(math.sin(1/x), 3) / (math.pow(x, 3) * math.log(1 + 1/x))
        return a * math.exp(-math.pow(x, 4)) + b * math.exp(-math.pow(x, -4))

def f1(x):
    if x == 0:
        return 0
    elif x == 1:
        return 0
    else:
        a = math.sin(3 * x) * math.atan(x) * math.pow(1 - x, 4) / (math.log(x) * (1 + math.pow(x, 4)))
        b = math.sin(3 / x) * math.atan(1 / x) * math.pow(x - 1, 4) / \
            (math.log(x) * (math.pow(x, 6) + math.pow(x, 2)))
        return a * math.exp(-math.pow(x, 2)) - b * math.exp(-math.pow(x, -2))

def f2(x):
    if x == 0:
        return 9
    else:
        a = (math.pow(x, 2) + 1) * math.pow(math.sin(3 * x), 2) / (math.log(1 + x) * x)
        b = (math.pow(x, 2) + 1) * math.pow(math.sin(3 / x), 2) / (math.log(1 + 1 / x) * math.pow(x, 2))
        return a * math.exp(-math.pow(x, 2)) + b * math.exp(-math.pow(x, -2))


def integrate(e, f):
    def kv_formula(a, b):
        if a > b:
            print("Wrong parameters")
        else:
            return (b - a) * (f(b) + f(a)) / 2
    res = [0, 0, 0]
    a, b = 0, 1
    h = 0.5
#    h = 0.0001
    while a + h <= b:
        while True:
            I1 = kv_formula(a, a + h)
            I11 = kv_formula(a, a + h/2)
            I21 = kv_formula(a + h/2, a + h)
            delta = (I11 + I21 - I1) / 3.0
            res[1] = res[1] + delta
            res[2] = res[2] + math.fabs(delta)
            if math.fabs(delta) > e:
                h = h / 2
#                print("h = ", h)
            else:
                break

        res[0] = res[0] + I1
        a = a + h
#       h = max(h, 0.00001)
#        if i % 1000 == 0:
#            print("next step = ", a)
    h = b - a
    res[0] = res[0] + kv_formula(a, a + h)
    return res



if __name__ == '__main__':
    f_ = f1
    e = math.pow(10, -3)
    I = integrate(e, f_)[0]
    print("Integral = ", I)

    e = math.pow(10, -7)
    res1 = integrate(e, f_)
    print("Integral-7 = ", res1[0])
    e = math.pow(10, -9)
    res2 = integrate(e, f_)
    print("Integral-9 = ", res2[0])
    e = math.pow(10, -11)
    res3 = integrate(e, f_)
    print("Integral-11 = ", res3[0])