\input epsf
\nopagenumbers
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\noindent {\bf Problem statement} A computer program reports the
following:

$$\int_0^1 {x\over{x+1}}\,dx=1-\ln 2\,;\qquad \int_0^\infty
{t\over{(2t+1)(t+1)^2}}\,dt=1-\ln 2\,.$$

\noindent Verify that the two integrals are equal. Notice that you are
{\it not}\/ asked to evaluate these definite integrals, only to
explain why the values are equal.

\medskip 

\noindent {\bf Hint} Find the antiderivatives and compute both
integrals: a very direct method.

\medskip 

\noindent {\bf (Hint)$^{\bf 2}$} Change one integral into the other:
$x$ goes from 0 to 1 and $t$, from $0$ to $\infty$ -- everything
involved is a rational function, so make the change from $x$ to $t$
with a simple rational function. After you find a suitable change of
variables, how does $dx$ change to $dt$?

\vfil\eject\end