I plugged rather basic integral into my new calculator (TI Nspire CX CAS) just to see what it could do. Surprisingly, it returned undef and I'm wondering if somebody could explain why and/or how I can fix this.
The integral I used is as follows
$$\int_0^\infty \frac{e^{\frac{-x}{y}}e^{-y}}{y}dx = e^{-y}$$ The calculator couldn't perform this, but when I replaced $y$ by a constant like the number 2 it was able to handle it, which I find strange. I presume it's assuming that $y$ can take a value of zero which would make it undefined.
—update—
Even after simplifying the integral and pulling constants out, it still cannot perform the integration
$$\frac{e^{-y}}{y}\int_0^\infty e^{\frac{-x}{y}}dx = e^{-y}$$
Best Answer
And what happens if $y = 0$? How is the calculator supposed to know what you mean for such a value?
Even if you defined the function $f(x,y) = e^{-x/y}e^{-y}/y$ in such a way as to make it meaningful at $y = 0$, there remains a fundamental misconception in your claim, easily tested when $y < 0$. What happens then?