Evaluate the Integral integral of -7t^-1 with respect to t

Problem

(∫_^)(−7*t(−1)*d(t))

Solution

1. Identify the constant and the variable part of the integrand.

2. Factor out the constant −7 from the integral.

(∫_^)(−7*t(−1)*d(t))=−7*(∫_^)(t(−1)*d(t))

3. Rewrite the term t(−1) as 1/t to recognize the standard integral form.

−7*(∫_^)(1/t*d(t))

4. Apply the rule for the integral of 1/t which is ln(t)

−7*ln(t)+C

Final Answer

(∫_^)(−7*t(−1)*d(t))=−7*ln(t)+C

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