Find the Antiderivative x^-1

Problem

(∫_^)(x(−1)*d(x))

Solution

1. Identify the expression as a power of x The expression x(−1) is equivalent to 1/x

2. Apply the rule for the antiderivative of the reciprocal function. The power rule for integration, (∫_^)(xn*d(x))=(x(n+1))/(n+1) cannot be used when n=−1 because it would result in division by zero.

3. Recall the logarithmic integration formula which states that the antiderivative of 1/x is the natural logarithm of the absolute value of x

4. Add the constant of integration C to represent the family of all possible antiderivatives.

Final Answer

(∫_^)(x(−1)*d(x))=ln(x)+C

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