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Grade 12Integral Calculus

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

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 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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