The ∫ex+e−xex−e−xlog⁡sinh⁡xdx=

∫coth⁡xlog⁡(sinh⁡x)dx =log⁡(log⁡(sinh⁡x))+c ∫f1(x)f(x)dx=log⁡|f(x)|+c

The ∫ex+e−xex−e−xlog⁡sinh⁡xdx=

∫coth⁡xlog⁡(sinh⁡x)dx =log⁡(log⁡(sinh⁡x))+c ∫f1(x)f(x)dx=log⁡|f(x)|+c

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The $\int \frac{e^{x} + e^{- x}}{(e^{x} - e^{- x} \log \sinh x} dx =$

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$\log | \cosh x | + c$

$\log (\log \cosh x) + c$

$\log (\log \sinh x) + c$

$log⁡ (\log (e^{x} + e^{- x})) + c$

answer is C.

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Detailed Solution

$\begin{array}{l} \int \frac{\coth x}{\log (\sinh x)} dx \\ = \log (\log (\sinh x)) + c \\ \int \frac{f^{1} (x)}{f (x)} dx = \log | f (x) | + c \end{array}$

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The $\int \frac{e^{x} + e^{- x}}{(e^{x} - e^{- x} \log \sinh x} dx =$