Question

Integrate

e^((-3x+2sinx)/6)

Answer 1

Thanks. It could be. Any indications would be helpful for me to investigate.

Answer 2

Wait. That 1/6 is part of the exponent?

Answer 3

Yes

Answer 4

You could have just left it and put 1/e^6 outside the integral.

Answer 5

exp ((-3x +2sinx)\div6)

Answer 6

Oh yah.

Answer 7

e^1/6 is the integral?

Answer 8

No. That's just a constant you can pull out of the integral

Answer 9

That still looks like a tough one.

Answer 10

yep haha

Answer 11

\[-1/2\exp ^{2sinx-3x}\]

Answer 12

That where i get to but can't find out what to do with 2sinx

Answer 13

Wolfram Alpha -
http://www.wolframalpha.com/input/?i=integrate+e%5E%282*sinx+-+3*x%29

Answer 14

daaamn. if wolfram cant do it then i'm not going to try

Answer 15

Are you supposed to get the indefinite integral or maybe an approximation of a definite integral?

Answer 16

I think that is simpler than it seems but I have missed a trick?

Answer 17

I need to get an indefinite integral

Answer 18

Ok. I may have found the issue. Does it make a difference if I have (2cosx-3)

Answer 19

with it

Answer 20

This function as written does not have a closed form answer.
Where did you get this integral?

Answer 21

this looks the same:
http://openstudy.com/study#/updates/4faf997ee4b059b524fa839e

Answer 22

so was i late?

Answer 23

I need to find the general solution to the following in implicit form

\[dy/dx = (2cosx -3) \exp ^{(1/6)(-3x+2sinx))} y ^{5/6} (y>0)\]

Answer 24

aha! that is easier i think, we have a substitution.

Answer 25

Of course that is easier. Why did you hide ( 2 cos x -3?

Answer 26

\[\int\limits{y^{\frac{-5}{6}}}dy = \int\limits{(2cosx - 3)e^{\frac{1}{6} (-3x + 2sinx)}}dx\]

u = -3x + 2sinx

Answer 27

And I use the substitution method?

Answer 28

yes.

Answer 29

@WonHungLo i think we were wrong when we said we could take that factor out earlier.

Answer 30

Thanks everybody. I can now investigate all this and see how we get to where we got to. I will need time but I am learning! YES!

Answer 31

@hmidante, please write down the whole question and not one part of it.