# Integration Of exponential Function

I have tried almost everything, but can't solve this integral.

$$\int e^{-1/x^2} \, dx$$

• thats not possible. why do you want to solve it? Commented Jun 28, 2015 at 17:35
• @supinf why not possible Commented Jun 28, 2015 at 17:52
• i don't know exactly why that is impossible, but somebody told me that there is no way to express the solution as a combination of elementary functions. Commented Jun 28, 2015 at 18:26
• @supinf so you wanna tell that no curve has slope of $e { ^(-1/x^2)}$ Commented Jun 28, 2015 at 19:19
• This anti-derivative cannot be expressed in terms of elementary functions. Why are you trying to solve this? Commented Jun 29, 2015 at 5:16

This statement is similar to the impossibility of solving a polynomial of degree $\geq$ 5 in terms of radicals; also the impossibility of "squaring the circle", namely constructing (in a finite number of steps) a square with straight edge and compass which has the same area of a given circle; also the impossibility of trisecting a given angle with just a straight edge and compass. The proofs of these statements can be learned through the topic of Galois theory.