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Question

Question: \[\log(1 + e^{x})\]...

log(1+ex)\log(1 + e^{x})

A

log(1+ex)- \log(1 + e^{- x})

B

log(1ex)- \log(1 - e^{- x})

C

log(ex+e2x)\log(e^{- x} + e^{- 2x})

D

None of these

Answer

log(1ex)- \log(1 - e^{- x})

Explanation

Solution

Let axxdx=\int_{}^{}{\frac{a^{\sqrt{x}}}{\sqrt{x}}dx =}

Therefore 2axlogea+c2a^{\sqrt{x}}\log_{e}a + c

2axlogae+c2a^{\sqrt{x}}\log_{a}e + c