$\int{ \frac{ 1 }{ t } } \mathrm{d} t$
Use $\int{ \frac{ 1 }{ x } } \mathrm{d} x=\ln\left({|x|}\right)$ to evaluate the integral$\ln\left({|t|}\right)$
Substitute back $t={e}^{x}-10{e}^{-x}$$\ln\left({|{e}^{x}-10{e}^{-x}|}\right)$
Simplify the expression$\ln\left({|{e}^{x}-\frac{ 10 }{ {e}^{x} }|}\right)$
Add the constant of integration $C \in ℝ$$\begin{array} { l }\ln\left({|{e}^{x}-\frac{ 10 }{ {e}^{x} }|}\right)+C,& C \in ℝ\end{array}$