solve an integral

#1
Hi there,

Is there any way of analytically solving the following integral?

int(exp(b0+b1*x)/(1+exp(b0+b1*x)) 1/m*exp(-x/m) , from, c to Inf). with respect to x?

where c>0,m>0, and b0,b1 real numbers.

I think the answer is no but I also need to be sure.
I've tried matlab with no luck, did some transformation by hand with no luck also..

If anyone is sure that the above can or cannot be anallytically solved please answer me!!

Thanx in advance!!
 

Dragan

Super Moderator
#2
Hi there,

Is there any way of analytically solving the following integral?

int(exp(b0+b1*x)/(1+exp(b0+b1*x)) 1/m*exp(-x/m) , from, c to Inf). with respect to x?

where c>0,m>0, and b0,b1 real numbers.

I think the answer is no but I also need to be sure.
I've tried matlab with no luck, did some transformation by hand with no luck also..

If anyone is sure that the above can or cannot be anallytically solved please answer me!!

Thanx in advance!!

The integral appears to be solvable if you impose the additional assumption that 0<b1<1.

However, the solution involves a hypergeometric function of (Mathematica) type:

Hypergeometric2F1[ 1, 1/(b1*m), 1 + 1/(b1*m), -Cosh[b0] + Sinh[b0] ].