integration: integrate( 1/(e^(t)+1)^(1/2)) dt=?

[Luke 1345]

question: integrate( 1/(e^(t)+1)^(1/2)) dt=?

can I directly let e^(t)=(tanx)^2 ?
I have tried this method and it will produce a +and- ans
or is there any better way to do this question?

 

[Deleted member 4993]

question: integrate( 1/(e^(t)+1)^(1/2)) dt=?

can I directly let e^(t)=(tanx)^2 ?
I have tried this method and it will produce a +and- ans
or is there any better way to do this question?

There are several possible substitution available for this problem

However, "tan" substitution is the easiest - in my opinion.