Question

Solve the integral:
1 / (e^x + 1)
Explain thoroughly the algebraic step that is necessary.

Answer 1

hmm....

Answer 2

\[\int\frac{1}{e^x+1}dx\]
if we had an e^x up top we could ln it

Answer 3

do we multiply by a conjugate?

Answer 4

add zero to the top?

Answer 5

add zero is what id try

Answer 6

\[\int\frac{1+(e^x-e^x)}{e^x+1}dx\]
\[\int\frac{1+e^x-e^x}{e^x+1}dx\]
\[\int\frac{1+e^x}{e^x+1}-\frac{e^x}{e^x+1}dx\]
\[\int\ 1-\frac{e^x}{e^x+1}dx\]
\[x - ln(e^x+1)+C\]

Answer 7

Nicely done, thanks.