\frac{4q^{2}}{\beta ^{2}r^{2d-4}}{)}\right)
\label{Lw}$$$$\zeta ={}_{2}{F_{1}}\left( {[1],\,\left[ {\frac{{5n-6}}{{2(n-1)}}}\right] ,\,%
}\frac{{L}_{W}}{{2(n-1)}}\right) ,\,  \label{Fzeta}$$

$$\eta ={}_{2}{F_{1}}\left( {\left[ {-\frac{1}{2},\,\frac{{-n}}{{2(n-1)}}}%
\right] ,\,\left[ {\frac{{n-2}}{{2(n-1)}}}\right] ,\,1-}\Gamma ^{2}\right) .
\label{Feta}$$

$$\Gamma =\sqrt{{1}+\frac{{q^{2}}}{{\beta ^{2}}{r^{2(n-1)}}}}$$

It was shown that the mentioned gauge potential reduce to that of Maxwell field for weak field limit $\beta \rightarrow \infty $. Considering a special case ${\alpha _{3}=}\frac{{{\alpha ^{2}}}}{{3(n-2)(n-3)(n-4)(n-5)}}$ and ${\alpha _{2}}=\frac{\alpha }{{(n-2)(n-3)}}$, we can show that the metric function$$f(r)=k+\frac{r^{2}}{\alpha }\left( 1-H^{1/3}\right) {,}  \label{fr}$$with$$H=1+\frac{{3\alpha m}}{{{r^{n}}}}+\frac{{6\alpha \Lambda }}{{n(n-1)}}+\frac{{%
3\alpha {\beta ^{2}}}}{{n(n-1){r^{n}}}}\times \left\{
\begin{array}{cc}
{{r^{n}}}+\frac{{2nq}}{{\beta }}{\int }\left( {{\sqrt{Lw}-{\frac{{1}}{\sqrt{%
Lw}}}}}\right) {dr}, & \text{ENED} \\
-{8{r^{n}}}+8{n}\int {\,{r^{n-1}}}\left[ \Gamma -{\ln \left( \frac{\Gamma {+1%
}}{2}\right) }\right] {dr}, & \text{LNED}%
\end{array}%
\right. ,  \label{gr}$$satisfies all components of the field equations (\[Geq\]). The parameter $%
m $ is an integration constant which is related to finite mass as [@ADM] $$M=\frac{V_{n-1}(n-1)m}{16\pi }.  \label{Mass}$$We should note that since computing the total mass leads to an infinite quantity, one may solve this problem by using of background subtraction method whose asymptotical geometry matches that of the solutions. Another approach comes from the fact that adding an additional surface action does not alter the bulk equations of motion. It is known as AdS/CFT inspired counterterm method [@Counterterm]. All methods have the same result and one may obtain the 