A. ln(1 + e^2u) + CB. 1/2 ln |1+e^u| + CC. 1/2 tan^-1 e^u + CD. tan^-1 e^u + CE. 1/2tan e^2u + C. Created by Claudia. science-mathematics-en - mathematics-en

Evaluate ∫ e^u / 1+e^u?

May 2021 2 129 Report

Evaluate ∫ e^u / 1+e^u?

A. ln(1 + e^2u) + C

B. 1/2 ln |1+e^u| + C

C. 1/2 tan^-1 e^u + C

D. tan^-1 e^u + C

E. 1/2tan e^2u + C

Let's use a U sub! (but I'm gonna use x instead because the problem is given in terms of u)

x=1+e^u

dx = e^u du

Integral( dx / x ) = ln(x) + c

= ln(1+e^u) + c

Confirmed with Wolfram:

Did you mistype something? The answer does not appear to be present.

Let v = e^u

dv = e^u du so dv = v du and du = dv/v

Substitute to get

integral ( e^u / 1+e^u du) =

integral ( v / 1+v dv/v)

= integral (1/(1+v) dv)

= ln|1 + v| + C

= ln|1 + e^u| + C

None of the listed answers are correct.