Find the Antiderivative f(x)=x^(1/3)

Problem

(∫_^)(x(1/3)*d(x))

Solution

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

2. Apply the formula by setting n=1/3 and adding 1 to the exponent.

n+1=1/3+1=4/3

3. Divide the expression by the new exponent 4/3

(x(4/3))/(4/3)+C

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

3/4*x(4/3)+C

Final Answer

(∫_^)(x(1/3)*d(x))=3/4*x(4/3)+C

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