Integration involving complex numbers

I am trying to Integrate this equation

$\displaystyle \int\frac{dx}{x^2-6x+34}

$

i have tried to factorise the polynomial on the denominator and thus

$\displaystyle x=\frac {-b\pm\sqrt {b^2-4c}}{2}=3\pm5i

$

where b = -6, c = 34

using my knowledge of complex functions this can be written as

$\displaystyle e^{3x} (c_1 cos 5x + c_2 sin 5x)

$

thus the integral can be written as

$\displaystyle \int\frac{dx}{e^{3x} (c_1 cos 5x + c_2 sin 5x)}$

not sure where to go now? any ideas?