Solving equation with integration using MATLAB

[kelvin490]

I would like to solve an equation below using MATLAB:

All the parameters except p are known, so I only need to solve for p. However since I need to consider the sign of the integrand and there is an absolute value sign in it I don't know how to solve it. Could anyone please help? Thank you.

 

[scottdave]

Consider different values of m. Is m an integer? If so, then you will have two cases:
You have sign(expression) * (abs(expression))^m
Odd m: sign(expression) * (abs(expression))^m is the same as (expression)^m

Even m: sign(expression) * (abs(expression))^m will have two choices:
if expression is positive, then the same as (expression)^m
if expression is negative, then the same as -(expression)^m

So see if you can split into cases like this and integrate in portions.