How should I integrate $e^{x^6-11x-66}$?

Question

I tried: $$ \begin{align*} \int e^{x^6-11x-66}dx &= \frac{e^{x^6-11x-66}\cdot(x^6-11x-66)}{(x^6-11x-66)} \\ &= e^{x^6-11x-66} \\ \end{align*} $$ Can this work?

Answer 1

No,

$$\left(e^{x^6-11x-66}\right)'\ne e^{x^6-11x-66}.$$

Besides, it is well known that the only function that is its own antiderivative is $e^x$.