Evaluate ∫ dx/(1 + e^-x).

Indefinite Integrals · Question 33 of 90

Question 33

HardOriginal question

Evaluate $\int \frac{dx}{1 + e^{-x}}$ .

\log\left(1 + e^{-x}\right) + C

Correct answerYour answer

x - \log\left(1 + e^{x}\right) + C

Correct answerYour answer

\log\left(1 + e^{x}\right) + C

Correct answerYour answer

x + e^{-x} + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Multiply top and bottom by $e^{x}$ : $\frac{1}{1 + e^{-x}} = \frac{e^{x}}{e^{x} + 1}$ .
The top is the derivative of the bottom: $\log(1 + e^{x}) + C$ .

Worth noting

$\log(1 + e^{-x})$ takes the bottom as it stands, but its derivative is $-e^{-x}$ , not the top.

Ten questions from Indefinite Integrals, at your own pace.

Ten questions from Indefinite Integrals, at your own pace.