numerically integrating an expression containing 'i'

edit

The integrand isn't a real for all (complex) values of x, though. If you wrap the symbolic part in an anonymous function that just does the evaluation (at real values of x in this integral) it will work:

sage: numerical_integral(lambda x: i*sin(i*x), 0, 0.2)
(-0.020066755619075848, 2.2278574117824245e-16)

Your integrand is -sinh(x) and so you can do this using integrate.

f(x)=i*sin(i*x)
print f(x).simplify()
integrate(f(x), x, 0, 0.2)

gives

-sinh(x)
-0.0200667556191