Q.

∫ex+e−x(ex−e−x)logsinh  x  dx  =

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a

log|cosh  x|+c

b

log(logcoshx)+c

c

log(logsinhx)+c

d

log(log(ex+e−x))+c

answer is C.

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Detailed Solution

log|sinhx|=t                  cothx dx= dt     ∫1t dt= log|t|+c =log|log(sinhx)|+c
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∫ex+e−x(ex−e−x)logsinh  x  dx  =