Integrate...

Question

Integrate...

anonymous · Answer

$$\int\limits_{}^{}\frac{ 1 }{ (\ln s) +4 }ds$$

anonymous · Answer

is there a way I'm forgetting that can simplify the denominator

hartnn · Answer

u can't simplify the denominator further.

anonymous · Answer

u substitution I don't think will work

hartnn · Answer

nopes, this integration is not standard.... answer involves exponential integral http://www.wolframalpha.com/input/?i=integral+1%2F%284%2Bln+x%29

amistre64 · Answer

u = lns + 4  ; s= e^(u-4)
du = 1/s ds
s du = ds
$$\int \frac{e^{u-4}}{u}du$$
it does seem a bit odd eh

amistre64 · Answer

we might be able to change that into a suitable taylor poly tho

anonymous · Answer

I see what you did. Very creative nice.

amistre64 · Answer

thnx :)  not sure how useful it is tho ....

anonymous · Answer

It is pretty messy. The real question was is this equation separable and thats what i got on one side. I was just curious what the integration would look like, but I didn't have to solve

amistre64 · Answer

just a bit more mashing it about

$$\int \frac{e^{u-4}}{u}du$$
$$\int \frac{e^{u}e^{-4}}{u}du$$
$$e^{-4}\int \frac{e^{u}}{u}du$$

anonymous · Answer

and no closed form for what amistre got

anonymous · Answer

I could use an explanation on how do identify a linear equation if you have the time. I have read the definition in the book and it is just not clicking

amistre64 · Answer

i have a test to take in 15 minutes, and a 10 minutes walk to get there :)  good luck

anonymous · Answer

A linear first order equation is an equation that can be expressed in the form$$a _{1}(x)\frac{ dy }{ dx }+a _{0}(x)y= b(x)$$

anonymous · Answer

Thanks good luck to you too.