Find the Integral x^(3/2)

Problem

(∫_^)(x(3/2)*d(x))

Solution

1. Identify the integration rule for power functions, which is the Power Rule for Integrals.

2. Apply the formula (∫_^)(xn*d(x))=(x(n+1))/(n+1)+C where n=3/2

3. Add 1 to the exponent to find the new power: 3/2+1=5/2

4. Divide the expression by the new exponent: (x(5/2))/(5/2)

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

6. Include the constant of integration C

Final Answer

(∫_^)(x(3/2)*d(x))=(2*x(5/2))/5+C

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