Evaluate the Integral integral of 34/(x^2) with respect to x

Problem

(∫_^)(34/(x2)*d(x))

Solution

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

(∫_^)(34*x(−2)*d(x))

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

34*(∫_^)(x(−2)*d(x))

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

34*((x(−2+1))/(−2+1))+C

4. Simplify the exponent and the denominator.

34*((x(−1))/(−1))+C

5. Simplify the expression by multiplying the constants and rewriting the negative exponent as a fraction.

−34*x(−1)+C

−34/x+C

Final Answer

(∫_^)(34/(x2)*d(x))=−34/x+C

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