  In this work we compute relative periods for B-branes, realized in terms of
divisors in a compact Calabi-Yau hypersurface, by means of direct integration.
Although we exemplify the method of direct integration with a particular
Calabi-Yau geometry, the recipe automatically generalizes for divisors in other
Calabi-Yau geometries as well. From the calculated relative periods we extract
double-logarithmic periods. These periods qualify to describe disk instanton
generated N=1 superpotentials of the corresponding compact mirror Calabi-Yau
geometry in the large volume regime. Finally we extract the integer invariants
encoded in these brane superpotentials.
