Final answer:
To find the general indefinite integral of the function x(1 + 7x⁴) dx, use the power rule for integration. The general indefinite integral is (1/2)x² + (7/4)x⁵ + C.
Step-by-step explanation:
To find the general indefinite integral of the function ∫ x(1 + 7x⁴) dx, we need to use the power rule for integration. The power rule states that the integral of x^n dx is equal to (1/(n+1))x^(n+1) + C, where C is the constant of integration.
For this problem, we have x(1 + 7x⁴), which can be written as x + 7x⁵. Using the power rule, we integrate x to get (1/2)x^(2+1) = (1/2)x², and we integrate 7x⁵ to get (7/4)x^(4+1) = (7/4)x⁵.
Therefore, the general indefinite integral of the function is (1/2)x² + (7/4)x⁵ + C, where C is the constant of integration.