Doubt from integrals

ignore post

a option

C option....

if u can find any mistake till this step please help me out

Even I had come till the second step. No, I don't have solution for this.

a option for sure correct please see its e^(-x)
instead of e^x at ln(..) in this term..
answer key pointing wrong answer..

Could be... Let's ask @Shwetanshu_2018 bhaiya...

I got 'c'. Posting in a minute.

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ooo sheesh i got my mistake @Samarth_2020
its should be 2ln3 instead of ln3 now c option is correct i apologise for my mistake..

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Your method is far better btw.

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I don’t think ,integration of 1/( e^x + 1 ) can be written as ln (e^x + 1)
For integrating this you need to split numerator into e^x +1 -e^x

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sir multiplied nd divide by e^(-x) then taken t to it.. @Shwetanshu_2018 bro will turn sane result..

That will result in
-ln (e^-x + 1 )
But you have written
-ln(e^x + 1)

sir i apologised for it in #post7