Evaluate the Integral integral of x^(5/2) with respect to x

Problem

(∫_^)(x(5/2)*d(x))

Solution

1. Identify the form of the integral as a power of x which follows the power rule for integration (∫_^)(xn*d(x))=(x(n+1))/(n+1)+C for n≠−1

2. Apply the power rule by adding 1 to the exponent n=5/2

5/2+1=7/2

3. Divide the expression by the new exponent 7/2

(x(7/2))/(7/2)+C

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

2/7*x(7/2)+C

Final Answer

(∫_^)(x(5/2)*d(x))=2/7*x(7/2)+C

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