Use a change of variables or the table to evaluate the following indefinite integral.
\[
\int x^{13} e^{x^{14}} d x
\]
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\[
\int x^{13} e^{x^{14}} d x=\square
\]

Step 1 ：Identify the integral is in the form of \(\int f'(x) e^{f(x)} dx\), where \(f(x) = x^{14}\) and \(f'(x) = 14x^{13}\).

Step 2 ：Use the formula \(\int f'(x) e^{f(x)} dx = e^{f(x)} + C\) to solve this integral.

Step 3 ：However, we need to adjust the coefficient of \(f'(x)\) to match the integral. The coefficient of \(x^{13}\) in the integral is 1, but the coefficient of \(x^{13}\) in \(f'(x)\) is 14.

Step 4 ：Therefore, we need to divide the result by 14.

Step 5 ：\(\int x^{13} e^{x^{14}} dx = \frac{1}{14}e^{x^{14}}\)

Step 6 ：Add the constant of integration, C, to the result.

Step 7 ：\(\boxed{\int x^{13} e^{x^{14}} dx = \frac{1}{14}e^{x^{14}} + C}\)