Discover MakerZone

MATLAB and Simulink resources for Arduino, LEGO, and Raspberry Pi

Learn more

Discover what MATLAB® can do for your career.

Opportunities for recent engineering grads.

Apply Today

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

Products

No products are associated with this question.

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

Contact us