How to solve an integral?

2012 1 7
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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,

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Andrew Newell
Andrew Newell 2012-1-7

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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.

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Vahid
Vahid 2012-1-7
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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Walter Roberson
Walter Roberson 2012-1-7

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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 2012-1-7

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

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