Evaluate the Integral integral of 9x^3 with respect to x

Problem

(∫_^)(9*x3*d(x))

Solution

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

2. Apply the constant multiple rule for integration by moving the constant 9 outside the integral.

(∫_^)(9*x3*d(x))=9*(∫_^)(x3*d(x))

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

9*(∫_^)(x3*d(x))=9⋅(x(3+1))/(3+1)+C

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

9⋅(x4)/4+C

5. Combine the terms into a single fraction.

(9*x4)/4+C

Final Answer

(∫_^)(9*x3*d(x))=(9*x4)/4+C

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