Find the Integral 5/(x^2)

Problem

(∫_^)(5/(x2)*d(x))

Solution

1. Rewrite the integrand using a negative exponent to make it easier to apply the power rule for integration.

(∫_^)(5*x(−2)*d(x))

2. Apply the constant multiple rule by moving the constant factor outside the integral.

5*(∫_^)(x(−2)*d(x))

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

5⋅(x(−2+1))/(−2+1)+C

4. Simplify the expression by performing the arithmetic in the exponent and the denominator.

5⋅(x(−1))/(−1)+C

5. Format the result by moving the negative sign and rewriting the negative exponent as a fraction.

−5/x+C

Final Answer

(∫_^)(5/(x2)*d(x))=−5/x+C

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