Evaluate the Integral integral of x^-3 with respect to x

Problem

(∫_^)(x(−3)*d(x))

Solution

1. Identify the form of the integral as a power function where the exponent n=−3

2. Apply the power rule for integration, which states that (∫_^)(xn*d(x))=(x(n+1))/(n+1)+C for any n≠−1

3. Substitute the value n=−3 into the power rule formula.

4. Simplify the exponent and the denominator by calculating −3+1=−2

5. Rewrite the expression in a simpler form by moving the negative exponent to the denominator if desired.

Final Answer

(∫_^)(x(−3)*d(x))=−1/(2*x2)+C

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