Find the Integral x^-3

Problem

(∫_^)(x^(−3)*d(x))

Solution

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

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

3. Substitute n=−3 into the formula to get (x^(−3+1))/(−3+1)+C

4. Simplify the exponent and the denominator to get (x^(−2))/(−2)+C

5. Rewrite the expression in a standard form by moving the negative exponent to the denominator.

Final Answer

(∫_^)(x^(−3)*d(x))=−1/(2*x^2)+C

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