Question

Find the indefinite integral:

Answer 1

\[\int\limits_{?}^{?}\frac{ e^{y} }{ 2-e^{y} } dy\]

Answer 2

i know i'll be using substitution.

Answer 3

Let\[u=2-e^y\]then\[du=?\]

Answer 4

e^y y dy?

Answer 5

\[u=2-e^y\implies du=-e^ydy\implies e^ydy=-du\]so what is the integral now?

Answer 6

\[\int\limits_{?}^{?} 1/du du\]

Answer 7

well minus?

Answer 8

how did you get two du's ?

Answer 9

\[\int\limits_{e^y}}^{2-e^{y}} e^{\]

Answer 10

\[\int\limits_{}^{} \frac{ e^{y} }{ 2-e{y} } e^{y}\]

Answer 11

where is the other e^y coming from?

Answer 12

thats my du.

Answer 13

well dy.

Answer 14

it should be negative.

Answer 15

is the answer ln|2-e^y|+c?

Answer 16

you dropped the negative sign, but aside from that the answer is correct