MATLAB: How to compute Laplace transforms when the time shift is a variable, in Symbolic Math Toolbox 5.7 (R2011b)

Symbolic Math Toolbox

I am working with Laplace transforms of functions involving sine waves and Heaviside functions. When I execute the following code:
% Numeric time shift
syms t w
x = sin(w*(t-10))*heaviside(t-10);
X = laplace(x);
pretty(simplify(X))
I receive the answer I expect:
w / ( exp(10 s) (s^2 + w^2 ) )
However, when there is one more symbolic variable, T instead of 10:
% Symbolic time shift
syms t w T
x = sin(w*(t-T))*heaviside(t-T);
X = laplace(x);
pretty(simplify(X))
I receive the following answer:
-laplace(sin(w (T - t)) heaviside(t - T), t, s)
How can I make the answer resemble what I received in the first case, with 'T' instead of 10?

Best Answer

You can impose the assumption that T is positive:
syms T positive
syms t w
x = sin(w*(t-T))*heaviside(t-T);
X = laplace(x);
pretty(simplify(X))
Then you can receive the following answer:
w / ( exp(T s) (s^2 + w^2) )