\ANG{
\begin{tabular}[t]{llll}
(a) $\D\int\limits_{0}^{1} x^{n}\,\RMd x$ & 
(b) $\D\int\limits_{0}^{\frac{\pi}{\omega}} A\sin \omega t\,\RMd t$ & 
(c) $\D\int\limits_{1}^{4} \frac{\RMd x}{x^{3}}$ & 
(d) $\D\int\limits_{-1}^{-2}\left(\frac{x^{5}}{3}-\frac{3}{x^{7}}\right)\,\RMd x$ 
\rule[-8mm]{0mm}{15mm}\\
(e) $\D\int\limits_{-\frac{\pi}{2}}^{\pi} \cos\frac{x}{3}\,\RMd x$ & 
(f) $\D\int\limits_{0}^{3}(x^{2}+1)(2x^{2}-x)\,\RMd x$  & 
(g) $\D\int\limits_{0}^{1} \sqrt[3]{x}\,\RMd x$ & 
(h) $\D\int\limits_{1}^{3}\frac{x^{2}+2x+1}{x^{4}+x^{3}}\,\RMd x$  
\end{tabular}
} 
\LSG{
\begin{enumerate}
\item $\D\int\limits_{0}^{1} x^{n}\,\RMd x=
  \biggl[\frac{x^{n+1}}{n+1}\biggl]_{0}^{1}=\frac{1}{n+1}$
\item $\D\int\limits_{0}^{\frac{\pi}{\omega}} A\sin \omega t\,\RMd t=
  \biggl[-\frac{A}{\omega}\cos\omega t\biggl]_{0}^{\frac{\pi}{\omega}}=
  -\frac{A}{\omega}\cos\pi+\frac{A}{\omega}\cos 0=\frac{2A}{\omega}$
\item $\D\int\limits_{1}^{4} \frac{\RMd x}{x^{3}}=
  \biggl[-\frac{1}{2x^{2}}\biggl]_{1}^{4}=-\frac{1}{2\cdot 4^{2}}+\frac 12=
  \frac{15}{32}$
\item $\D\int\limits_{-1}^{-2}\left(\frac{x^{5}}{3}-\frac{3}{x^{7}}\right)\,\RMd x=
  \biggl[\frac{x^{6}}{18}+\frac{1}{2x^{6}}\biggl]_{-1}^{-2}=
  \frac{32}{9}+\frac{1}{128}-\frac{1}{18}-\frac{1}{2}=\frac{385}{128}$
\item $\D\int\limits_{-\frac{\pi}{2}}^{\pi} \cos\frac{x}{3}\,\RMd x=
  \biggl[3\sin\frac x3\biggl]_{-\frac{\pi}{2}}^{\pi}=
  3\left[\sin\frac{\pi}{3}+\sin\frac{\pi}{6}\right]=\frac 32\left(1+\sqrt{3}\right)$
\item $\D\int\limits_{0}^{3}(2x^4 - x^3 + 2x^2 - x)\,\RMd x=
  \biggl[\frac{2x^{5}}{5}-\frac{x^{4}}{4}+\frac{2x^{3}}{3}-
   \frac{x^{2}}{2}\biggl]_{0}^{3}=\frac{1809}{20}=90{,}45$
\item $\D\int\limits_{0}^{1} x^{\frac 13}\,\RMd x=
  \biggl[\frac 34\,x^{\frac 43}\biggl]_{0}^{1}=\frac 34$
\item \begin{align*}\int\limits_{1}^{3}\frac{x^{2}+2x+1}{x^{4}+x^{3}}\,\RMd x&=
  \int\limits_{1}^{3}\frac{(x+1)^{2}}{x^{3}(x+1)}\,\RMd x=
  \int\limits_{1}^{3}\left(\frac{1}{x^{2}}+\frac{1}{x^{3}}\right)\,\RMd x=\\
  &= \biggl[-\frac{1}{x}-\frac{1}{2x^{2}}\biggl]_{1}^{3}=
  -\frac 13-\frac{1}{18}+1+\frac 12=\frac{10}{9}
\end{align*}
\end{enumerate}
}
