Question

integrate e^(-6x)sin(e^(-3x))dx

Answer 1

did you try substuting
u = e^(-3x) ?

Answer 2

*substituting

Answer 3

yes I tried it by parts and I'm not getting the right answer.....

Answer 4

by parts, after that substitution, right ?

Answer 5

\[\int\limits e ^{-6x}\sin(e ^{-3x})dx\]

Answer 6

what do you mean?

Answer 7

note
e^(-6x) = e^(-3x) * e^(-3x)

Answer 8

i mean , you plug in
u = e^-3x

also find du

Answer 9

sin e^-3x becomes sin u

Answer 10

-1/3du=e^(-3x)dx

Answer 11

yesss

Answer 12

-1/3 integral u sin u du

did u get that ?

Answer 13

yes I did =)

Answer 14

can you finish now ?
let me know if you have any other doubts on this :)

Answer 15

so from here I would use integration by parts?

Answer 16

yes
but if you can, i suggest you use standard result directly

Answer 17

ok how would I do that ?

Answer 18

ok, use integration by parts then

Answer 19

or
\(\int x \sin x dx = -x \cos x +\sin x + c\)

Answer 20

ok thank you so much!!!

Answer 21

welcome ^_^
and
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