solution for integration of following expression.

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Dr. Siva Malla
Dr. Siva Malla 2012-9-25
can any one solve this integration?
integration of ((exp(a*x))/(1+b*exp(c*x)));

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Babak
Babak 2012-9-25
A general form for the indefinite integral of your problem does not exist.
Take y = exp(a*x) and transform the integral over x to an integral over y. It will be the integral of
1/a* 1/(1+b*y^(c/a)) *dy
depending on what the value of c/a is, a general form for the integral may/may not exist. For example, for c/a=1, the result is
1/(a*b)* log(1+b*y)
but for c/a=2, b>0, the integral will be
sqrt(b)/a*Arctan(sqrt(b)*y)
So I don't think you can get a general form of the integral from the Symbolic Math Toolbox or any other Symbolic Math Software. You can use the numerical integrations methods and integrate it over a definite domain.
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Matt Fig
Matt Fig 2012-9-25
I am not sure that is what the OP asked for here. I asked above for clarification, but got none.

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Azzi Abdelmalek
Azzi Abdelmalek 2012-9-25
syms x
% you must assign values to a b and c to find result
a=1;b=1;c=1;
y=((exp(a*x))/(1+b*exp(c*x)))
inty=int(y)
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Babak
Babak 2012-9-25
Thanks! It confirms the result of
1/(a*b)* log(1+b*y)
for the case where c/a=1 in my answer above. I don't think MATLAB can do the integral when a, b and c are all syms though...

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