Find the Antiderivative f(x)=1/(x^2)

Problem

(∫_^)(1/(x2)*d(x))

Solution

1. Rewrite the integrand using a negative exponent to prepare for the power rule.

1/(x2)=x(−2)

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

(∫_^)(x(−2)*d(x))=(x(−2+1))/(−2+1)+C

3. Simplify the exponent and the denominator.

(x(−1))/(−1)+C

4. Rewrite the expression back into fraction form for the final result.

−x(−1)+C=−1/x+C

Final Answer

(∫_^)(1/(x2)*d(x))=−1/x+C

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