I'm trying to evaluate the following integral;
$$\int e^{(x^2 – z^2)} (2x \cos(2xz) – 2z \sin(2xz)) dz$$
I've tried splitting it up, and using integration by parts, but it just isn't coming out in a simple way. I've been stuck on this for hours. I'm sure there's some rule or trick I can use, but I'm really not sure.
Any assistance would be fantastic. 🙂
Best Answer
Hint: Observe that the first $e^{x^2}$ factors out of the integral. After removing it, notice that what you have looks sort of like the output of a product rule. Can you work backwards to find the product?