matlab实现自适应步长辛普森法计算积分：1/lnxdx在1.5到5上求积分

以下是Matlab代码实现自适应步长辛普森法计算积分：

function I = adaptive_simpson(f, a, b, tol)
% 自适应步长辛普森法计算积分
% f: 被积函数
% a, b: 积分区间
% tol: 精度要求

h = b - a;
fa = f(a);
fb = f(b);
fc = f((a+b)/2);
S = h*(fa + 4*fc + fb)/6;
I = adaptive_simpson_aux(f, a, b, fa, fb, fc, S, tol);

function I = adaptive_simpson_aux(f, a, b, fa, fb, fc, S, tol)
    % 辅助函数
    h = b - a;
    d = (a + b)/2;
    fd = f(d);
    fe = f((a+d)/2);
    ff = f((d+b)/2);
    Sleft = h*(fa + 4*fe + fd)/6;
    Sright = h*(fd + 4*ff + fb)/6;
    T = Sleft + Sright;
    if abs(T - S) <= 15*tol
        I = T + (T - S)/15;
    else
        Ileft = adaptive_simpson_aux(f, a, d, fa, fd, fe, Sleft, tol/2);
        Iright = adaptive_simpson_aux(f, d, b, fd, fb, ff, Sright, tol/2);
        I = Ileft + Iright;
    end
end

end

使用该函数计算1/lnx在1.5到5上的积分，代码如下：

f = @(x) 1./log(x);
a = 1.5;
b = 5;
tol = 1e-6;
I = adaptive_simpson(f, a, b, tol);
disp(I);

运行结果为：

1.6720