Question Number 142681 by mnjuly1970 last updated on 03/Jun/21
![prove that :: 𝛗:=∫_0 ^( ∞) ((ln(1+cos(x)))/(1+e^( x) ))dx=0 ................](https://www.tinkutara.com/question/Q142681.png)
$$ \\ $$$$\:\:\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}:=\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left(\mathrm{1}+{cos}\left({x}\right)\right)}{\mathrm{1}+{e}^{\:{x}} }{dx}=\mathrm{0} \\ $$$$\:\:\:\:\:……………. \\ $$$$ \\ $$
Commented by Dwaipayan Shikari last updated on 04/Jun/21
![Seems to be 0. But there is little spike on the positive half](https://www.tinkutara.com/question/Q142735.png)
$${Seems}\:{to}\:{be}\:\mathrm{0}.\:{But}\:{there}\:{is}\:{little}\:{spike}\:{on}\:{the}\:{positive}\:{half}\: \\ $$
Commented by Dwaipayan Shikari last updated on 04/Jun/21
![](https://www.tinkutara.com/question/20787.png)