S²x⁴dx -¹

To solve the expression you've provided, \( \int S^2 x^4 \, dx \), we first need to clarify the meaning of \( S \) in this context. If \( S \) represents a constant, the integral can be computed as follows: 1. Factor out the constant \( S^2 \) from the integral: \[ \int S^2 x^4 \, dx = S^2 \int x^4 \, dx \] 2. Now, we compute the integral of \( x^4 \): \[ \int x^4 \, dx = \frac{x^{4+1}}{4+1} + C = \frac{x^5}{5} + C \] 3. Substituting this back into our equation gives: \[ S^2 \int x^4 \, dx = S^2 \left( \frac{x^5}{5} + C \right) = \frac{S^2 x^5}{5} + C' \] where \( C' \) is a constant of integration. Thus, the result of the integral \( \int S^2 x^4 \, dx \) is: \[ \frac{S^2 x^5}{5} + C' \] If \( S \) has a different meaning or if more context is needed, please provide further details!