radial geometry gradient calculation

I have two functions alpha1 and alpha 2. I want to calculate beta1 and beta 2 by solving the equation below.

alpha=-gradient(beta)

for each beta and alpha functions separately. The functions are in radial coordinates. I have tried by best in the code below. However my calculations ar not correct. Any help is appreciated.

Thanks GH

clc
clear all

r1 = 1;                          
r2 = 3;
R=linspace(r1,r2,100);

for i = 1:100
    alpha1(i) = (15*log(R(i)/r2))/log(r1/r2);
end

for i = 1:100
    alpha2(i) = 5;
end

figure(1)
plot(R,alpha1,R,alpha2)
xlabel('r');
ylabel('\alpha');
legend('\alpha1','\alpha2')

beta1=-cumtrapz(alpha1,R); 
beta2=-cumtrapz(alpha2,R); 

figure(2)
plot(R,beta1,R,beta2)
xlabel('r');
ylabel('\beta');
legend('\beta1','\beta2')