MATLAB: symbolic integral of symfun

Question

I wish to perform a symbolic integration over time; the code is given below.

syms x1 u1 t
x1 = symfun(sym('x1(t)'), [t]);
x1dot = p1 + p4*p8 - p13*x1;
int(x1dot,t)

The answer should be:

e^(-p13*t)*x1(0)+(p1 + p4*p8)/(-p13)*[1-e^(-p13*t)]

what I get is:

Warning: Explicit integral could not be found. 

ans(t) =

int(p1 - p13*x1(t) + p4*p8*u1(t), t)

It seems to me that it does not recognize that x1dot is the derivative of x1. How can I solve this issue?

Answer 1

What you are trying to do is not strictly speaking integration, i.e. from a known function f(t) deduce a function F(t) such that the derivative of F is f. The original function is not really known, since it depends on itself (no matter how trivial the relationship might seem to a human, you need to inverse it).

It is rather solving a differential equation, for which dsolve is probably the way to go. MATLAB has no way to guess that x1dot is the derivative of x1. I guess you could declare x1dot=diff(x1) but why not use diff(x1) directly where needed ?