Solving the Integral of Exp Function with Tips and Tricks

[damjanisa]

Hi every body

I've tryed to solve this integration but I can not. Please if anyone can help plsease DO HELP.

Integral of { Exp(-x-(t/(a+bx)))dx} from 0 to infinity.

Thanks for any help

 

[BrendanH]

There doesn't seem to be any immediate solution to this problem... are you sure you've written/interpreted it correctly?

 

[damjanisa]

YES I AM SURE
i KNOW IT IS hard to solve it but I hope some one can DO IT

 

[cristo]

Why do you think a solution must exist? Have you tried with a computer algebra package first, to check that the integral does exist?

 

[Schrodinger's Dog]

?

But my maths program fires out.

$$\int e^{[-x-(\frac{t}{a+bx})]}\:dx\rightarrow\int e^{[-x-(\frac{t}{a+bx})]}\:dx$$

As a general solution. Which generally means there isn't one.

 

[dextercioby]

Does this baby $\int_{0}^{\infty} \mbox{exp}\left(-\frac{1}{x}\right) {} \ dx$ exist in $\mathbb{R}$ ? If so, can you compute it ?

 

[damjanisa]

I found this integration in on of published paper in the mobile communication section.

by using matlab: int(exp(-1/x)) = x*exp(-1/x)-Ei(1,1/x), and

int(exp(-1/x),0,inf) , ans = Inf,

I thanks all of you whose trying to help me.

hoever, I hope this will add some knowledge to all of us.

Thans again.

 

[Schrodinger's Dog]

I found this integration in on of published paper in the mobile communication section.

by using matlab: int(exp(-1/x)) = x*exp(-1/x)-Ei(1,1/x), and

int(exp(-1/x),0,inf) , ans = Inf,

I thanks all of you whose trying to help me.

hoever, I hope this will add some knowledge to all of us.

Thans again.

Ah so the Exponential/log integral function turns up again. Problem with that is most maths programs will not give that as a solution. Mine didn't, and it is perfectly capable of churning out the exponential log function as an answer(see here):

https://www.physicsforums.com/showthread.php?t=224473

See this thread for the logarithmic integral.

http://mathworld.wolfram.com/LogarithmicIntegral.html

Thanks damjanisa that was quite an education.

 

[damjanisa]

Hi, Schrödinger's Dog

THANKS FOR YOUR REPLAY.

However, I tried to undestand what you have said but I can not. I don't know may because I have more than one thing to do these days. I'm sorry.

I understood there is a solution to this integration but I can not know how I do it.
Please if you have more time give me some hints or more explanation.

BEST REGARDS DEAR

 

[Schrodinger's Dog]

Did you check the links, they explain the function. If the answer is infinite the only other solution would be some sort of expansion. Is that what you are looking for?