Find the Antiderivative x^(1/3)

Problem

(∫_^)(x(1/3)*d(x))

Solution

1. Identify the expression as a power function of the form xn where n=1/3

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

3. Add one to the exponent: 1/3+1=4/3

4. Divide by the new exponent: (x(4/3))/(4/3)

5. Simplify the fraction by multiplying by the reciprocal of the denominator.

6. Add the constant of integration C

Final Answer

(∫_^)(x(1/3)*d(x))=(3*x(4/3))/4+C

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