Evaluate of each of the following integral: `int_(-pi//3)^(pi//3)1/(1+e^x)dx`

Explanation

Let,`int_(-pi//3)^(pi//3)1/(1+e^x)dx`

`(1+e^x)=t`

`dx=dt/(t-1)`

=`int_(-pi//3)^(pi//3) dt/(t(t-1))`

=`int_(-pi//3)^(pi//3)(1/(t-1)-1/t)dt`

=`int_(-pi//3)^(pi//3)(log(t-1)-log(t))`


=`int_(-pi//3)^(pi//3)log((e^x)/(e^x+1))-log(1/(1+e^(-x))))`

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