Find the Integral 1/(y^2)

Problem

(∫_^)(1/(y2)*d(y))

Solution

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

1/(y2)=y(−2)

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

(∫_^)(y(−2)*d(y))=(y(−2+1))/(−2+1)+C

3. Simplify the exponent and the denominator.

(y(−1))/(−1)+C

4. Rewrite the expression back into fraction form with a positive exponent.

−y(−1)+C=−1/y+C

Final Answer

(∫_^)(1/(y2)*d(y))=−1/y+C

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