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Determine the antiderivative of 6xⁿ for n≠−1 with respect to x.

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Final answer:

The antiderivative of 6x^n for n not equal to -1 is 6 times x raised to the power of (n+1) divided by (n+1) plus the constant of integration, C.

Step-by-step explanation:

To determine the antiderivative of 6x^n for n≠-1, we use the power rule of integration, which states that the antiderivative of x^n is x^(n+1)/(n+1) plus the constant of integration, C. Following this rule, the antiderivative is 6 times the antiderivative of x^n, so we integrate as follows:

∫ 6x^n dx = 6 * ∫ x^n dx = 6 * (x^(n+1) / (n+1)) + C

Where:
n is any real number except -1, and
C is the constant of integration.

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