A family of logarithm integrals Let , where p is a real
Chapter 1, Problem 51RE(choose chapter or problem)
A family of logarithm integrals Let \(I(p)=\int_{1}^{e} \frac{\ln x}{x^{p}} \ d x\), where p is a real number.
a. Find an expression for I(p) for all real values of p.
b. Evaluate \(\lim _{p \rightarrow \infty} I(p)\) and \(\lim _{p \rightarrow-\infty} I(p)\).
c. For what value of p is I(p)=1?
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