Evaluate the Integral integral of x^(-3/2) with respect to x

Problem

(∫_^)(x(−3/2)*d(x))

Solution

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

2. Apply the power rule by adding 1 to the exponent and dividing by the new exponent.

3. Calculate the new exponent: −3/2+1=−1/2

4. Divide the expression by the new exponent: (x(−1/2))/(−1/2)

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

6. Add the constant of integration C

Final Answer

(∫_^)(x(−3/2)*d(x))=−2*x(−1/2)+C

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