№2237
\(
\int\limits_{0}^{1}\left(e^x-1\right)^4e^xdx
=\int\limits_{0}^{1}\left(e^x-1\right)^4d\left(e^x-1 \right)
=\left.\frac{\left(e^x-1\right)^5}{5}\right|_{0}^{1}
=\frac{(e-1)^5}{5}
\)
№2239
\(
\int\limits_{0}^{1}\frac{xdx}{\left(x^2+1\right)^2}
=\frac{1}{2}\cdot\int\limits_{0}^{1}\left(x^2+1\right)^{-2}d\left(x^2+1\right)
=-\frac{1}{2}\cdot\left.\frac{1}{x^2+1}\right|_{0}^{1}
=\frac{1}{4}.
\)