Question

int \frac{ e ^{3x} }{(1+e ^{3x} )^{8}} dx

Answer 1

let \[u =1+e^{3x}\rightarrow du =3e^{3x}dx\] and solve as usual

Answer 2

ok, thats where i got

Answer 3

is it 1/u^8 ?

Answer 4

\[\int\frac{e^3x}{(1+e^{3x})^8}dx\]is it yours?

Answer 5

yes

Answer 6

ok, so i was thinking right....

Answer 7

yes, it turns \[\int \frac{1}{3}u^{-8}du\]

Answer 8

oh ok,...thats what i didnt see

Answer 9

so, you can step up from now, right?

Answer 10

yes, just substitute and that is final answer, right?

Answer 11

u can go to denominator

Answer 12

take integral of this, it s\[\frac{1}{3}\frac {u^{-7}}{(-7)} + C\\=\frac{-1}{21u^7}+C\\=\frac{-1}{21(1+e^{3x})^7}\]

Answer 13

+ C at last

Answer 14

great. your awsome. thanks

Answer 15

yw