How to solve an integral?

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,

Answer 1

[Andrew Newell]

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.

[Vahid]

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!

Answer 2

[Walter Roberson]

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) .

Answer 3

[Vahid]

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