Evaluate the Integral integral of x^-2 with respect to x

Problem

(∫_^)(x(−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 and dividing by the new exponent.

3. Substitute n=−2 into the formula.

(∫_^)(x(−2)*d(x))=(x(−2+1))/(−2+1)+C

4. Simplify the arithmetic in the exponent and the denominator.

(∫_^)(x(−2)*d(x))=(x(−1))/(−1)+C

5. Rewrite the expression using a positive exponent and moving the negative sign to the front.

(∫_^)(x(−2)*d(x))=−1/x+C

Final Answer

(∫_^)(x(−2)*d(x))=−1/x+C

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