Find the Antiderivative 3x^3

Problem

(∫_^)(3*x3*d(x))

Solution

1. Identify the integral as a power rule problem where the function is ƒ(x)=3*x3

2. Apply the constant multiple rule by moving the constant 3 outside of the integral sign.

(∫_^)(3*x3*d(x))=3*(∫_^)(x3*d(x))

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

3*(∫_^)(x3*d(x))=3⋅(x(3+1))/(3+1)+C

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

3⋅(x4)/4+C

5. Combine the constant and the fraction into a single coefficient.

3/4*x4+C

Final Answer

(∫_^)(3*x3*d(x))=3/4*x4+C

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