Use a change of variables or the table to evaluate the following indefinite integral. \( \int x^{3} e^{x^{4}} d x \) \( \int x^{3} e^{x^{4}} d x=\square \)

To solve the integral \( \int x^{3} e^{x^{4}} d x \), we can use a change of variables. Let's set \( u = x^4 \). Then, the derivative \( du = 4x^3 dx \), or \( dx = \frac{du}{4x^3} \). The integral becomes: \[ \int x^{3} e^{x^{4}} d x = \int x^{3} e^{u} \frac{du}{4x^{3}} = \frac{1}{4} \int e^{u} du \] Now, integrating \( e^{u} \) gives us \( e^{u} + C \). Re-substituting \( u = x^4 \): \[ \frac{1}{4}(e^{x^{4}} + C) = \frac{1}{4} e^{x^{4}} + C \] So, the final result is: \[ \int x^{3} e^{x^{4}} d x = \frac{1}{4} e^{x^{4}} + C \]