Evaluate the Integral integral of 5/(x^3) with respect to x

Problem

(∫_^)(5/(x3)*d(x))

Solution

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

(∫_^)(5*x(−3)*d(x))

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

5⋅(x(−3+1))/(−3+1)+C

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

5⋅(x(−2))/(−2)+C

4. Format the result by moving the negative exponent back to the denominator and simplifying the fraction.

−5/(2*x2)+C

Final Answer

(∫_^)(5/(x3)*d(x))=−5/(2*x2)+C

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