MATLAB: Numerical integration twice wrt same variable

Question

Hello people,

I have afunctionand it is calculated by only numerical methods. As an example let's say;

where

And I am asked to calculate; at some points of x, let's say at

I do not how to it. I need to calculate y, and use it as a function of x by numerical integration methods. I write my algortihm down below, and I get of course error. Can someone help me fix it?

Thanks in advanced.

clear
clc
r = 1:5; x = 1:5;
for k = 1:length(x)
y(k) = integral(@(r) ((r+1).^2+1)./r,1,x(k))
I(k) = integral(@(x) (1+y(k)),0,1)
end

Answer 1

fun1 = @(x)integral(@(r)((r+1).^2+1)./r,1,x);
fun2 = integral(@(x)(1+fun1(x)),0,1,'ArrayValued',true)