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evaluate the following integral ∫ 1 / e^(x) + 1 dx

evaluate the following integral
∫ 1 / e^(x) + 1 dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello student,
Please find the answer to your question below

I = \int \frac{1}{e^{x}+1}dx
I = \int \frac{e^{x}+1-e^{x}}{e^{x}+1}dx
I =\int dx - \int \frac{e^{x}}{e^{x}+1}dx
I = x - \int \frac{e^{x}}{e^{x}+1}dx
e^{x} + 1 = t
e^{x}dx = dt
I = x - \int \frac{dt}{t}
I = x - log(t) + c
I = x - log(e^{x}+1) + c

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