Find the Antiderivative x^(1/2)

Problem

(∫_^)(x^(1/2)*d(x))

Solution

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

2. Apply the formula by setting n=1/2

3. Add 1 to the exponent: $1/2 + 1 = 3/2$.

4. Divide the expression by the new exponent 3/2 which is equivalent to multiplying by its reciprocal 2/3

5. Include the constant of integration C

Final Answer

(∫_^)(x^(1/2)*d(x))=(2*x^(3/2))/3+C

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