Find the Integral x^(1/3)

Problem

(∫_^)(x(1/3)*d(x))

Solution

1. Identify the power rule for integration, which states that for any constant n≠−1 the integral of xn is (x(n+1))/(n+1)+C

2. Apply the formula by substituting n=1/3 into the power rule expression.

3. Add the exponent values where 1/3+1=4/3

4. Simplify the coefficient by calculating the reciprocal of the new exponent, which is 1/(4/3)=3/4

5. Include the constant of integration C to represent the family of antiderivatives.

Final Answer

(∫_^)(x(1/3)*d(x))=(3*x(4/3))/4+C

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