Question

evaluate the indefinite integral

Answer 1

\[\int\limits_{?}^{?} e^u/(1-e^u) du\]

Answer 2

by using subtitution

Answer 3

Note that setting x = e^u gives \[ \displaystyle\int \frac {\mathrm{d}x}{1 - x}. \]Do you know how to evaluate this?

Answer 4

no

Answer 5

but doesnt u= 1-e^u

Answer 6

he left

Answer 7

you could do x=1-e^u

Answer 8

do you know why i wouldn't name it u
because there is already a u in (1-e^u)

Answer 9

your right

Answer 10

so what do i do next?

Answer 11

find dx

Answer 12

how?

Answer 13

by differentiating x=1-e^u

Answer 14

Using x = e^u gives \[ \displaystyle\int \frac {\mathrm{d}x}{1 - x} = - \ln \left| 1 - x \right| + \mathcal{C}. \]Now substitute back in x = e^u.

Answer 15

dx/du=?

Answer 16

dx=-e^u

Answer 17

dx=-e^u du

Answer 18

you could also say -dx=e^u du

Answer 19

okay then i plug in and i get