Evaluate the Integral integral of -24x^5 with respect to x

Problem

(∫_^)(−24*x5*d(x))

Solution

1. Identify the constant and the power of x in the integrand.

2. Apply the constant multiple rule by moving the constant −24 outside the integral.

(∫_^)(−24*x5*d(x))=−24*(∫_^)(x5*d(x))

3. Apply the power rule for integration, which states that (∫_^)(xn*d(x))=(x(n+1))/(n+1)+C for n≠−1

−24*(∫_^)(x5*d(x))=−24⋅(x(5+1))/(5+1)+C

4. Simplify the expression by performing the addition in the exponent and the denominator.

−24⋅(x6)/6+C

5. Divide the constant coefficient −24 by 6

−4*x6+C

Final Answer

(∫_^)(−24*x5*d(x))=−4*x6+C

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