Question

(e^(6x))/(e^(6x) + 1)

Answer 1

?

Answer 2

Integration problem

Answer 3

let u=e^(6x)+1 then what is du/dx

Answer 4

6e^(6x)
so, dx = 1/(6e^6x) du

Answer 5

where is the 1 coming from

Answer 6

du = 6e(6x) dx
or dx = (1/(6e^(6x)) du

Answer 7

It'd be helpful if you could present integration problems either in Equation Editor or by drawing them in the Draw utility, below.\[\int\limits_{}^{}\frac{ e ^{6x} dx }{ 1+e ^{6x} }\]

Answer 8

remember d/dx of e^x= itself

Answer 9

Try this please: let u = 1 + e^(6x).

Find du/dx. Unfortunately, your 6e(6x) is not correct. See magepkr's advice, above.

Solve this for du.

Answer 10

Examples:\[\frac{ d }{ dx }e^x=e^x\]

Answer 11

i think pat meant,
\(\Large dx = \dfrac{1}{6e^{6x}}du\)
which is correct

Answer 12

pat, you now have everything needed for substitution.
go ahead and tell us what u get?

Answer 13

Examples:\[\frac{ d }{ dx }e ^{3x}=e ^{3x}*\frac{ d }{ dx }3x=??\]

Answer 14

To summarize: Let u be defined as follows:\[u=1+e ^{6x}\]

Answer 15

Then\[\frac{ du }{ dx }=e ^{6x}*6\]so that \[du=6e ^{6x}dx,\]

Answer 16

1/6 ᶘ 1 /(e^u +1) du
= 1/6 (tan^-1 (e^u) =?

Answer 17

or \[\frac{ du }{ 6 }=e ^{6x}dx\]

Answer 18

Substitute du/6 for e^(6x) dx in the numerator.

Substitute u for \[1+e ^{6x}\]

Answer 19

in the denom. What do y ou get from doing this, Pat?