\ANG{
(a)\quad$\D\int (ax+b)^{99}\RMd x$\qquad
(b)\quad$\D\intop_1^{2}\frac{3x^2}{x^3+1}\,\RMd x$\qquad
(c)\quad Berechne $x$:\quad$\D\intop_2^{x}\frac{\RMd t}{t}=1$
} 
\LSG{
\begin{enumerate}
\item $\D\int (ax+b)^{99}\RMd x=\frac{(ax+b)^{100}}{100a}+C$
\item $\D\intop_1^{2}\frac{3x^2}{x^3+1}\,\RMd x=
\intop_1^{2}\frac{(x^3+1)'}{x^3+1}\,\RMd x=
\left[\ln|x^3+1|\right]_1^{2}=\ln 9-\ln 2\approx 1{,}50$
\item $\D\intop_2^{x}\frac{\RMd t}{t}=\ln x-\ln 2=\ln\frac x2=1\QDQ
x=2\e$
\end{enumerate}
}
