What is the function y if dy/dx=1/(e^x+1)?

To find the function y, we'll have to determine the
indefinite integral of the given function dy/dx.

I'll
suggest to replace e^x by t.

e^x = t => x = ln
t

We'll differentiate both
sides:

dx = dt/t

We'll
re-write the integral in t:

Int dx/(e^x+1) = Int
dt/t*(t+1)

We'll decompose the fraction 1/t(t+1) in a
difference of partial fractions.

1/t(t+1) = 1/t -
1/(t+1)

Int dt/t*(t+1) = Int dt/t - Int
dt/(t+1)

Int dt/t*(t+1) = ln |t| - ln|t+1| +
C

We'll apply quotient rule of
logarithms:

Int dt/t*(t+1) = ln |t/(t+1)| +
C

The primitive function is: y = Int
dx/(e^x+1) = ln e^x/(e^x+1) + C.