Question

Exciting Integral Problem

Answer 1

\[\frac{ e^{3x} }{ 1+e^{6x} }dx\]

Answer 2

the squigly thing is supposed to be in front

Answer 3

Hint: \(\displaystyle\int\dfrac{e^{3x}}{1+e^{6x}}\,dx = \int \frac{e^{3x}}{1+(e^{3x})^2}\,dx\).

Do you see how to proceed from here? :-)

Answer 4

Yeah I got to that step and now I don't know what to do

Answer 5

What methods of integration are you familiar with?

Answer 6

Guess and check

Answer 7

That's method right?

Answer 8

Well...you want to actually make a substitution here. Are you familiar with how to do that method?

Answer 9

how about u substetutien u=1+e^6x

Answer 10

Oh I know substitution. Let me try that and get back to you

Answer 11

Okay; what substitution would you make in this instance? :-)

Answer 12

lol exciting

Answer 13

It would be something like \[\frac{ du^{1/2} }{ u }\]

Answer 14

u = e^3x, looks like inverse tan is what you'll get?

Answer 15

you are in for a treat if this is excting

Answer 16

ohhh
hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Answer 17

okay I understand

Answer 18

-.- its just ln 1+(e^3x)^2

Answer 19

No, it isn't. \(\displaystyle \int\frac{1}{1+u^2}\,du \neq \ln (1+u^2)+C\)

Answer 20

Yeah I forgot about inverse tan

Answer 21

See look how excited all of you are. This is great. Thanks Internet strangers

Answer 22

oh i see

Answer 23

When you make the substitution \(u=e^{3x}\), we see that
\[\int\frac{e^{3x}}{1+e^{6x}}\,dx = \frac{1}{3}\int\frac{1}{1+u^2}\,du = \frac{1}{3}\arctan u + C = \frac{1}{3}\arctan(e^{3x})+C.\]

Answer 24

yeah

Answer 25

silly billy

Answer 26

wooooot. Alright

Answer 27

Gonna ace this math test

Answer 28

lol

Answer 29

My second suggestion was for e^3*x, that's what dan was thinking of I think, that's why I mentioned it haha but yeah definitely inverse tan :)

Answer 30

Dan's a nooooob

Answer 31

hey there is something interesting though

Answer 32

How did you even see inverse tan? I was just like "What is math?"

Answer 33

Because I'm batman

Answer 34

You found some evidence. You should watch the college humor videos on batman. all of them

Answer 35

this sh1t is so easy, i cant believe u 99's are choking so hard

Answer 36

I've seen it Ark :P

Answer 37

Nice. They are funny