# Difficult Integral

Tags:
1. Oct 10, 2016

### Prof. 27

1. The problem statement, all variables and given/known data
Hi, I'm doing a variation of parameters problem for my differential equations class. It requires solving the integral:

∫ex t-2 dt

I am sure my professor did not give me an impossible integral and that there is some algebraic "trick" to solving it, but despite going through several iterations of integration by parts I am unable to find it (I have encountered similar problems before but my memory of them is fuzzy).

2. Relevant equations
None

3. The attempt at a solution
Several Integration by parts attempts. I looked for a cancellation.

2. Oct 10, 2016

### LCKurtz

Both $x$ and $t$ in there?

Please give us a statement of the original problem and your work so far. How do we know your integral is correct?

3. Oct 10, 2016

### Staff: Mentor

If you have written the integral correctly, it's a very simple one to evaluate. Here ex can be treated as a constant.

4. Oct 10, 2016

### Prof. 27

Oh I'm so sorry! I mis-wrote the integral. It is:

∫e-x2 x-2 dt

5. Oct 10, 2016

### Ray Vickson

If you mean $\int e^{-x^2} x^{-2} \, dt$, that is easy: it is $e^{-x^2} x^{-2} \int dt = e^{-x^2}x^{-2} (t+C)$. If you mean $\int e^{-x^2}x^{-2} \, dx$, that is a different matter entirely. The integral is do-able in terms of the so-called error function.

On the other hand, if in the first form above the $x$ is a function of $t$, the integral may be intractable for certain functions $x = x(t)$.

Last edited: Oct 10, 2016