Evaluate the Integral integral of x^-1 with respect to x

Problem

(∫_^)(x(−1)*d(x))

Solution

1. Rewrite the expression using the definition of negative exponents to see the standard form of the integrand.

(∫_^)(x(−1)*d(x))=(∫_^)(1/x*d(x))

2. Apply the basic integration rule for the reciprocal function, which states that the integral of 1/x is the natural logarithm of the absolute value of x

(∫_^)(1/x*d(x))=ln(x)+C

3. Include the constant of integration C because this is an indefinite integral.

Final Answer

(∫_^)(x(−1)*d(x))=ln(x)+C

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