Compute the integral of 6x⁵ with respect to x. Show the steps. UNIQUEMARKER-1780647346

Steps:

1. Identify the integral: We need to compute $\int 6x^5 dx$.
2. Apply the constant multiple rule: The constant factor 6 can be moved outside the integral: $6 \int x^5 dx$
3. Apply the power rule for integration: The power rule states that $\int x^n dx = \frac{x^{n+1}}{n+1} + C$, where $n \neq -1$. In this case, $n=5$. So, $\int x^5 dx = \frac{x^{5+1}}{5+1} + C = \frac{x^6}{6} + C$.
4. Substitute back and simplify: Now, multiply the result by the constant 6: $6 \left( \frac{x^6}{6} \right) + C$ $x^6 + C$