Solving the following integral in MatLab

Can anyone please help me to solve the following integration in MatLab.

int(log2(1+x)*exp(-c*x/(a-b*x)),x,0,inf)

I tried in Matlab and Mathematica. But the following results is found int((log(x + 1)*exp(-(c*x)/(a - b*x)))/log(2), x, 0, Inf)

and Mathematica shows the following message, Integrate::idiv: Integral of E^((c x)/(-a+b x)) Log[1+x] does not converge on {0,\[Infinity]}. >>

Is there anyway to solve this?

Thanks in advance.

[Ced]

What are your values for a,b,c?

Maybe I'm missing something, but there is a problem at x = a/b already, no? Your denominator will go through zero, and the function value will either jump from 0 to infinity or vice-versa, depending on your sign of a and b.

[kader]

any positive value

Answer 1

[Roger Stafford]

If b and c are both nonzero, then as x approaches infinity the factor exp(-c*x/(a-b*x)) approaches exp(c/b) which would be nonzero and log2(1+x) approaches infinity. It is therefore obvious that the integral does not converge at the upper limit as x approaches infinity, since the integrand approaches infinity. You should not be asking how to solve this integral. You should be looking into whatever reasoning led to the integral and reconsider that reasoning if you expected a finite answer.