  The eigenvalues of the potentials
$V_{1}(r)=\frac{A_{1}}{r}+\frac{A_{2}}{r^{2}}+\frac{A_{3}}{r^{3}}+\frac{A_{4
}}{r^{4}}$ and
$V_{2}(r)=B_{1}r^{2}+\frac{B_{2}}{r^{2}}+\frac{B_{3}}{r^{4}}+\frac{B_{4}}{r^
{6}}$, and of the special cases of these potentials such as the Kratzer and
Goldman-Krivchenkov potentials, are obtained in N-dimensional space. The
explicit dependence of these potentials in higher-dimensional space is
discussed, which have not been previously covered.
