  A study of b semileptonic decays into D, D pi+- and D* pi+- final states is
presented. The D0, D+ and D*+ mesons are exclusively reconstructed in Z decay
data recorded from 1992 to 1995 in the DELPHI experiment at LEP. The overall
branching fractions are measured to be:
  BR(b -> D^0 \ell^- \bar{\nu}_{\ell} X) = (7.04 +/- 0.34 (stat) +/- 0.36
(syst.exp) +/- 0.17 (BR_D))%
  BR(b -> D^+ \ell^- \bar{\nu}_{\ell} X) = (2.72 +/- 0.19 (stat) +/- 0.16
(syst.exp) +/- 0.18 (BR_D))%
  BR(b -> D^{*+} \ell^- \bar{\nu}_{\ell} X) = (2.75 +/- 0.17 (stat) +/- 0.13
(syst.exp) +/- 0.09 (BR_D))%
  where the D0 and D+ results include also contributions from D*0 and D*+
decays. A fit to the distribution of the pi+- impact parameter to the primary
interaction vertex provides a measurement of the b semileptonic branching
fractions into the D0 pi+- X, D+ pi+- X and D*+ pi+- X final states. Assuming
that single pion decay modes of B mesons dominate, the partial rates for
\bar{B} -> D \pi \ell^- \bar{\nu_{\ell}} and \bar{B} -> D^{*} \pi \ell^-
\bar{\nu_{\ell}} have been obtained, corresponding to a total branching
fraction:
  BR(\bar{B} -> D \pi \ell^- \bar{\nu_{\ell}}) + BR(\bar{B} -> D^{*} \pi \ell^-
\bar{\nu_{\ell}}) = (3.40 +/- 0.52 (stat) +/- 0.32 (syst))% .
  This result agrees well with the observed difference between the total B
semileptonic branching fraction and the sum of the \bar{B} -> D \ell^-
\bar{\nu_{\ell}} and D^* \ell^- \bar{\nu_{\ell}} branching fractions.
