Answer
0
Work Step by Step
If $f(x)$ is odd $[\text { that is } f(-x)=-f(x)],$ then:
\[
\begin{array}{c}
0=\int_{-a}^{a} f(x) d x\\
\int_{0}^{\ln 2} \int_{-1}^{1} \sqrt{e^{y}+1} \tan x d x d y \\
=\int_{0}^{\ln 2} \sqrt{e^{y}+1} d y \int_{-1}^{1} \tan x d x=0
\end{array}
\]
Because it is integral of an odd function over [-1,1] , the result is 0.
