Evaluate the following improper integrals.

a$.{\displaystyle \underset{1}{\overset{15}{}}}\frac{dx}{\sqrt[\phantom{2}]{(x-1)(15-x)}}$

b$.{\displaystyle \underset{1}{\overset{}{}}}\frac{dx}{e^{x2}{e}^{4-x}}$

a$.$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.{\displaystyle \underset{1}{\overset{15}{}}}\frac{dx}{\sqrt[\phantom{2}]{(x-1)(15-x)}}=($Type an exact answer.$)$

B$.$ The improper integral diverges.