# How do you evaluate the integral #int e^t/(e^t+1)dt#?

# int \ (e^t)/(e^t+1) \ dt = ln(e^t+1)+C #

We want to find:

We can perform a simple substitution; Let

If we perform the substitution then we get:

And restoring the substitution we get:

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To evaluate the integral (\int \frac{e^t}{e^t+1} dt), use the substitution method. Let (u = e^t + 1), then (du = e^t dt). Substituting these into the integral, we get:

[ \int \frac{e^t}{e^t+1} dt = \int \frac{1}{u} du ]

This integral is now straightforward to solve:

[ \int \frac{1}{u} du = \ln|u| + C = \ln|e^t + 1| + C ]

where (C) is the constant of integration.

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