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solution for integration of following expression.

Asked by Siva Malla on 25 Sep 2012

can any one solve this integration?

integration of ((exp(a*x))/(1+b*exp(c*x)));

3 Comments

Matt Fig on 25 Sep 2012

Do you want the indefinite integral, or the integral over a certain range, or what?

Siva Malla on 26 Sep 2012

I want indefinite integral

Matt Fig on 26 Sep 2012

Then you will have to look to Mathematica.

Siva Malla

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2 Answers

Answer by Babak on 25 Sep 2012
Accepted answer

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.

1 Comment

Matt Fig on 25 Sep 2012

I am not sure that is what the OP asked for here. I asked above for clarification, but got none.

Babak
Answer by Azzi Abdelmalek on 25 Sep 2012
 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)

4 Comments

Azzi Abdelmalek on 25 Sep 2012
 inty=log(exp(x) + 1)
Babak on 25 Sep 2012

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...

Matt Fig on 25 Sep 2012

No, but Mathematica can:

Result

Azzi Abdelmalek

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