I have to calculate the following integral: $$I(\textbf{r})=\int d\textbf{r'} \frac{1}{|\textbf{r'}-\textbf{r}|}\cdot e^{-2r'-\lambda |\textbf{r'}-\textbf{r}|}$$
I thought of rewriting
$$|\textbf{r'}-\textbf{r}| = \sqrt{r'^2+r^2-2rr'\cos(\theta')}$$
Is that actually allowed to rotate the coordinate system like that and integrate for this specific function? So is it allowed to set the angle between the two vectors to $\theta'$.