Evaluate the following integrals. intfrac{e^x+e^{-x}}{e^x-e^{-x}}dx

Evaluate the following integrals. intfrac{e^x+e^{-x}}{e^x-e^{-x}}dx

Question
Integrals
asked 2020-11-08
Evaluate the following integrals.
\(\int\frac{e^x+e^{-x}}{e^x-e^{-x}}dx\)

Answers (1)

2020-11-09
\(\text{To evaluate}\)
\(I=\int\frac{e^x+e^{-x}}{e^x-e^{-x}}dx\)
\(\text{Let }e^x-e^{-x}=t\)
\(\text{Differentiating both sides}\)
\((e^x+e^{-x})dx=dt\)
\(I=\int\frac{e^x+e^{-x}}{e^x-e^{-x}}dx\)
\(I=\int\frac{1}{t}dt\)
\(I=\ln(t)+C\)
\(I=\ln(e^x-e^{-x})+C\)
0

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