Don't worry
Leibniz's integral rule
Differentiation under the integral sign - Wikipedia, the free encyclopedia
You do not need to use complex numbers
Here is an example of Leibniz's Rule in use
http://www.mathhelpforum.com/math-he...77-post19.html
And here is the complete thread: http://www.mathhelpforum.com/math-he...tegrals-2.html