Question

Integral

Answer 1

\[\int\limits_{}^{} \frac{ 8 }{ e ^{3x}} dx\]

Answer 2

I know its easy but I have trouble with which one to substitute

Answer 3

change its form by taking the e term to the top with a negative exponent.

Answer 4

ohh

Answer 5

8 is a constant, you can pull that out

Answer 6

no substitution just write 1/ e^(3x) = e^(-3x)

Answer 7

hartnn is one of my mentors... so he can help too

Answer 8

oh cool

Answer 9

I like to take the constants to the front too, just like @completeidiot

Answer 10

\[∫\frac{8}{e^{3x}}dx=8∫\frac{1}{e^{3x}}dx=8∫e^{-3x}dx\]

Answer 11

that's the ticket!

Answer 12

now u sub the exponent

Answer 13

u= -3x ?

Answer 14

yeah

Answer 15

du=-3dx

Answer 16

dx=-1/3du

Answer 17

or you can use
\[\huge{\int\limits_{}^{}e^{ax}dx =\frac{e^{ax}}{a}+c}\]

Answer 18

nice! slow down... make her work for it :)

Answer 19

That is a rule?

Answer 20

lol

Answer 21

:( i was just using standard rule.

Answer 22

basically u=ax in that case
they just solved it out

Answer 23

you do your steps.... hartnn is advanced

Answer 24

Haha

Answer 25

He teaches me on this forum.

Answer 26

ok,i will leave this upto u all. sorry for disturbing.

Answer 27

You wern't Im just slow haha

Answer 28

I love your company... you are always welcome as far as I'm concerned.

Answer 29

\[8∫{e^{-3x}dx\]
ok sooooo
u=-3x
we also need to change dx into du, in order to integrate properly
du=-3dx
dx=-1/3du

we substitute u and du into the equation
\[-\frac{1}{3}*8∫{e^{u}}du\]

now integrate
\[∫{e^{u}}du\]

Answer 30

This is my 4th problem with her... she's working... she just takes a little time.

Answer 31

@completeidiot is totally on it... he is saving the (-8/3) for the next step.