How to solve an integral?

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Vahid
Vahid on 7 Jan 2012
Dear all,
I am trying to solve the following integral with the use of the Symbolic Math Toolbox of the MATLAB:
syms b x;
int(tan(b*atan(x)),x);
but MATLAB gives the following warning:
Warning: Explicit integral could not be found.
I would be grateful if anybody would suggest how to overcome the problem.
Thanks in advance,

Accepted Answer

Andrew Newell
Andrew Newell on 7 Jan 2012
If you get that warning from the Symbolic Math Toolbox, it may mean that there really is no symbolic solution. You could still integrate it numerically for specific values of b using quadl.
  1 Comment
Vahid
Vahid on 7 Jan 2012
Since this integral is a part of my main integral problem which is related to finding the trajectory of a particle, it would be nice if I could somehow have a symbolic solution if there is!

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More Answers (2)

Walter Roberson
Walter Roberson on 7 Jan 2012
Nope, no integral in general. There are some (non-zero) cases that I can give answers for, but those have to do with various complex values for x and the answers in the situations are that the integral is undefined. No useful simplification for x and b real, just
i*(-x+2*(int(1/(exp((2*i)*b*atan(x))+1), x)))
where "i" is sqrt(-1) .

Vahid
Vahid on 7 Jan 2012
Thanks a lot! Fortunately, I got a straightforward integral by solving my problem in the hyperbolic coordinates :-D

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