  We investigate the infrared contribution from supermassive black hole
activity versus host galaxy emission in the mid to far-infrared (IR) spectrum
for a large sample of X-ray bright active galactic nuclei (AGN) residing in
dusty, star-forming host galaxies. We select 703 AGN with L_X = 10^42-46 ergs/s
at 0.1 < z < 5 from the Chandra XBootes X-ray Survey with rich multi-band
observations in the optical to far-IR. This is the largest sample to date of
X-ray AGN with mid and far-IR detections that uses spectral energy distribution
(SED) decomposition to determine intrinsic AGN and host galaxy infrared
luminosities. We determine weak or nonexistent relationships when averaging
star-formation activity as a function of AGN activity, but see stronger
positive trends when averaging L_X in bins of star-forming activity for AGN at
low redshifts. We estimate an average dust covering factor of 33% based on
infrared SEDs and bolometric AGN luminosity, corresponding to a Type 2 AGN
population of roughly a third. We also see a population of AGN that challenge
the inclination based unification model with individual dust covering factors
that contradict the nuclear obscuration expected from observed X-ray hardness
ratios. We see no strong connection between AGN fractions in the IR and
corresponding total infrared, 24 um, or X-ray luminosities. The average
rest-frame AGN contribution as a function of IR wavelength shows significant
(~80%) contributions in the mid-IR that trail off at lambda > 30 um.
Additionally, we provide a relation between observed L_X and pure AGN IR output
for high-z AGN allowing future studies to estimate AGN infrared contribution
using only observed X-ray flux density estimates.
