We find all real-valued general solutions
$f:S\rightarrow \mathbb{R}$
of the d’Alembert functional equation with involution
$$\begin{eqnarray}\displaystyle f(x+y)+f(x+\unicode[STIX]{x1D70E}y)=2f(x)f(y) & & \displaystyle \nonumber\end{eqnarray}$$
for all
$x,y\in S$
, where
$S$
is a commutative semigroup and
$\unicode[STIX]{x1D70E}~:~S\rightarrow S$
is an involution. Also, we find the Lebesgue measurable solutions
$f:\mathbb{R}^{n}\rightarrow \mathbb{R}$
of the above functional equation, where
$\unicode[STIX]{x1D70E}:\mathbb{R}^{n}\rightarrow \mathbb{R}^{n}$
is a Lebesgue measurable involution. As a direct consequence, we obtain the Lebesgue measurable solutions
$f:\mathbb{R}^{n}\rightarrow \mathbb{R}$
of the classical d’Alembert functional equation
$$\begin{eqnarray}\displaystyle f(x+y)+f(x-y)=2f(x)f(y) & & \displaystyle \nonumber\end{eqnarray}$$
for all
$x,y\in \mathbb{R}^{n}$
. We also exhibit the locally bounded solutions
$f:\mathbb{R}^{n}\rightarrow \mathbb{R}$
of the above equations.