\(\text{To evaluate}\)

\(I=\int\frac{e^x+e^{-x}}{e^x-e^{-x}}dx\)

\(\text{Let }e^x-e^{-x}=t\)

\(\text{Differentiating both sides}\)

\((e^x+e^{-x})dx=dt\)

\(I=\int\frac{e^x+e^{-x}}{e^x-e^{-x}}dx\)

\(I=\int\frac{1}{t}dt\)

\(I=\ln(t)+C\)

\(I=\ln(e^x-e^{-x})+C\)

\(I=\int\frac{e^x+e^{-x}}{e^x-e^{-x}}dx\)

\(\text{Let }e^x-e^{-x}=t\)

\(\text{Differentiating both sides}\)

\((e^x+e^{-x})dx=dt\)

\(I=\int\frac{e^x+e^{-x}}{e^x-e^{-x}}dx\)

\(I=\int\frac{1}{t}dt\)

\(I=\ln(t)+C\)

\(I=\ln(e^x-e^{-x})+C\)