  Many exclusive $c\to d/s\ell^+\nu_\ell~(\ell=e,\mu,\tau)$ transitions have
been well measured, and they can be used to test the theoretical calculations.
Motivated by this, we study the $D\to P/V/S\ell^+\nu_\ell$ decays induced by
the $c\to d/s\ell^+\nu_\ell$ transitions with the SU(3) flavor symmetry
approach, where $P$ denotes the pseudoscalar meson, $V$ denotes the vector
meson, and $S$ denotes the scalar meson with a mass below $1$ $GeV$. The
different decay amplitudes of the $D\to P\ell^+\nu_\ell$, $D\to
V\ell^+\nu_\ell$ or $D\to S\ell^+\nu_\ell$ decays can be related by using the
SU(3) flavor symmetry and by considering the SU(3) flavor breaking. Using the
present data of $D\to P/V/S\ell^+\nu_\ell$, we predict the not yet measured or
not yet well measured processes in the $D\to P/V/S\ell^+\nu_\ell$ decays. We
find that the SU(3) flavor symmetry approach works well in the semileptonic $D
\to P/V\ell^+\nu_\ell$ decays. For the $D \to S\ell^+\nu_\ell$ decays, only the
decay $D^+_s\to f_0(980)e^+\nu_e$ has been measured, the branching ratios of
the $D^+_s\to f_0(980)e^+\nu_e$ and $D\to S(S\to P_1P_2)\ell^+\nu_\ell$ decays
are used to constrain the nonperturbative parameters and then predict not yet
measured $D \to S\ell^+\nu_\ell$ decays, in addition, the two quark and the
four quark scenarios for the light scalar mesons are analyzed. The SU(3) flavor
symmetry predictions of the $D \to S\ell^+\nu_\ell$ decays need to be further
tested, and our predictions of the $D \to S\ell^+\nu_\ell$ decays are useful
for probing the structure of light scalar mesons. Our results in this work
could be used to test the SU(3) flavor symmetry approach in the semileptonic
$D$ decays by the future experiments at BESIII, LHCb and BelleII.
