Finite Sum of Exponential Integrals and the Harmonic Number

Daily Problem1 i's
Evaluate the integral0ekxdx,k>0,and computek=1100ekxdx.\text{Evaluate the integral} \int_{0}^{\infty} e^{-kx}\,dx, \quad k>0, \\ \text{and compute} \sum_{k=1}^{10} \int_{0}^{\infty} e^{-kx}\,dx.
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