This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
The integral of 6x^5 with respect to x is x^6 + C. Steps: 1. Identify the integral: We need to compute 6x^5 dx. 2. Apply the constant multiple rule: The constant factor 6 can be moved outside the integral: 6 x^5 dx 3. Apply the power rule for integration: The power rule states that x^n dx = x^n+1n+1 + C, where n ≠ -1. In this case, n=5. So, x^5 dx = x^5+15+1 + C = (x^6)/(6) + C. 4. Substitute back and simplify: Now, multiply the result by the constant 6: 6 ( (x^6)/(6) ) + C x^6 + C