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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2007 • Question 8

Question

Math 6420 • PDE Fall 2007 • Question 8

Evaluate the integral \[ I=\int _0^\infty \frac {x^\alpha \,dx}{(x+1)^2} \] (where \(\alpha \) is a constant parameter, so that the integral converges).

Raw LaTeX

Evaluate the integral
\[
  I=\int_0^\infty\frac{x^\alpha\,dx}{(x+1)^2}
\]
(where \(\alpha\) is a constant parameter, so that the integral converges).

Topic Tags

Cauchy Integral Formula and Integral Theorems Harmonic Functions and Poisson Integral Formula Linear Programming and Optimization Real Integral Evaluation by Complex Methods