Integrate: $\int \large\frac{2}{3} \frac{e^x \sqrt {e^x-4}}{e^x+g}$$dt$

Question

\[\begin {array} {1 1} (a)\;\frac{6 \sqrt 2}{5}-26 \tan ^{-1} \bigg(\sqrt {\frac{8}{13}}\bigg) \\ (b)\;\frac{8 \sqrt 2}{3}-\frac{52}{3} \tan ^{-1} \bigg(\sqrt {\frac{8}{13}}\bigg) \\ (c)\;\frac{2 \sqrt 2}{4}-39 \tan ^{-1} \bigg(\sqrt {\frac{8}{13}}\bigg) \\ (d)\;\frac{8 \sqrt 2}{5}-\frac{52}{3} \sin ^{-1} \bigg(\sqrt {\frac{8}{13}} \bigg) \end {array}\]