Integration of a multiplied weibull distribution

Question

I am having trouble integrating a weibull function multiplied with a production function. The expression shortened for integration is as follows:

$$v^{k+2}e^{-\left(\frac{v}{y}\right)^k}$$

I hope you can read the expression and help with the question.

Answer 1

First changing variable $v=y \text { }z$, the integral becomes slightly nicer and the final result is $$-\frac{1}{2} y^{k+3} \Gamma \left(\frac{k+3}{2},\frac{v^2}{y^2}\right)$$