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Integrate ∫[ 1 / e x + 1] dx

Integrate
∫[ 1 / ex + 1] dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Hello Student,
Please find 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 (1 - \frac{e^{x}}{e^{x} + 1})dx
I = x - log(e^{x}+1) + c
I = log(e^{x}) - log(e^{x}+1) + c
I = log(\frac{e^{x}}{e^{x} + 1}) + c

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