Matrix manipulation instead of loops

I have the following matrix form $[J]$:

$$\begin{bmatrix} \{ v,p + v\}\\ \{v, p + v, 2 p + v\} \\ \{v, p + v,2 p + v, 3 p + v\}\\ \{v, p + v,2 p + v, 3 p + v\} \\ \vdots \end{bmatrix}$$

I need to operate the list of each row by Max and Integrate and then add them all together like this:

$H=\int\limits_{0}^{\infty} \max \{ v,p + v\}dF(p)+\int\limits_{0}^{\infty} \max \{v, p + v, 2 p + v\}dF(p)+\dots$

I would like to use matrix operations to do it instead of loops, but I can't find a way to make it work.

Any help is appreciated. Thanks

• Do you know each v[i] values; Total[Integrate[Max[#], {p, 0, Infinity}] & /@ J] ? – OkkesDulgerci Mar 25 '18 at 16:25
• all except the last one, from H I will solve the last value v – Rodrigo Mar 25 '18 at 16:29
• I see. Can you post actual vector values if it is not too long. What is the length of J? – OkkesDulgerci Mar 25 '18 at 16:34
• I couldn't by pass the code formatting thing here is a link with a picture of J with n=10, at some point I would want to go for n=100 Matrix – Rodrigo Mar 25 '18 at 16:51