Integration involving complex numbers

• Oct 24th 2009, 08:53 PM
Karl Harder
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?
• Oct 24th 2009, 09:24 PM
mr fantastic
Quote:

Originally Posted by Karl Harder
I am trying to Integrate this equation

$\displaystyle \int\frac{dx}{x^2-6x+34}$$\displaystyle i have tried to factorise the polynomial on the denominator and thus \displaystyle x=\frac {-b\pm\sqrt {b^2-4c}}{2}=3\pm5i$$\displaystyle$

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)$$\displaystyle$

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?

$\displaystyle x^2 - 6x + 34 = (x - 3)^2 + 25$. This should suggest a standard form to you, especially if you first make the substitution $\displaystyle u = x - 3$.