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We measure the branching ratio of the purely leptonic decay of the D+ mesonwith unprecedented precision as B(D+ -> mu+ nu) = (3.82 +/- 0.32 +/-0.09)x10^(-4), using 818/pb of data taken on the psi(3770) resonance with theCLEO-c detector at the CESR collider. We use this determination to derive avalue for the pseudoscalar decay constant fD+, combining with measurements ofthe D+ lifetime and assuming |Vcd| = |Vus|. We find fD+ = (205.8 +/- 8.5 +/-2.5) MeV. The decay rate asymmetry [B(D+ -> mu+ nu)-B(D- -> mu- nu)]/[B(D+ ->mu+ nu)+B(D- -> mu- nu)] = 0.08 +/- 0.08, consistent with no CP violation. Wealso set 90% confidence level upper limits on B(D+ -> tau+ nu) < 1.2x10^(-3)and B(D+ -> e+ nu) < 8.8x10^(-6).

Precision Measurement of B(D+ -> mu+ nu) and the Pseudoscalar Decay Constant fD+