How to find a limit of a integral I want to calculate this limit of a integral
$$
\lim_{y \rightarrow 0}\int_0^1\frac{\exp(xy+x+y+1)}{xy+1} dx 
$$
I want to find a dominating function on the integrand. But I can't find a function $M(x)$ such that $f(x,y) \leq M(x)$. Do you guys have any ideas?

You can first restrict $y$ to $|y|\leq 1/2$, and then we have $|xy|\leq 1/2$ for all $x\in[0,1]$ and hence $1/(xy+1)$ has no singularity and it can be bounded by $2$.
For then $\exp(xy+x+y+1)\leq\exp(2x+2)$ and $2\exp(2x+2)$ is integrable on $[0,1]$. 
