Evaluate the Integral integral of 4/(x^3) with respect to x

Problem

(∫_^)(4/(x3)*d(x))

Solution

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

(∫_^)(4*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

4⋅(x(−3+1))/(−3+1)+C

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

4⋅(x(−2))/(−2)+C

4. Divide the coefficients and rewrite the expression with a positive exponent.

−2*x(−2)+C

−2/(x2)+C

Final Answer

(∫_^)(4/(x3)*d(x))=−2/(x2)+C

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