The value of
\[
\int_{0}^{\infty}\frac{x^{2}(1-x^{2})}{(1+x)^{24}}\,dx
\]
is
Show Hint
For integrals over \((0,\infty)\),
\[
\boxed{x\rightarrow\frac1x}
\]
is a useful substitution. If the integrand changes sign under this transformation, then the integral is
\[
\boxed{0.}
\]