Can someone quickly tell me what the integral of 1 over e^y(x) is

I have a seperable DE im trying to solve.

 

 

Pook (:

There is no general form for that integral. If you specify a function for y(x) I might be able to help.

If you would pose y(x) = x^2 it is even known that there is no analytic expression (in terms of standard functions) for the integral, other than int_0^x exp(z^2) dz ofcourse.

 

Mandrake

Im struggling with the intergration of 'e' aswell!

 

70e^(-0.1t)

 

Have no idea, can anyone help!

If you mean that the function is with respect to t (obviously ) then just make it a u substitution.

 

In detail: Let u = -0.1t

Then, du/-0.1=dt

 

Now solve for (integral)70e^u du

in general

 

[math]\int{ae^{bx}}dx=\frac{a}{b}e^{bx}+k[/math]

The other way to look at it to "guess" which function differentiates to give the function you're integrating. i.e. guess [math]\tfrac{1}{a} e^{ax}[/math]. Then if you differentiate this, you get your integral, so that's your answer.