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\begin{document}
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\center{\Large 11. MATEMATIKA A1 FELADATSOR}

\begin{enumerate}
\item Határozza meg az alábbi integrálokat parciális integrálással:
\begin{enumerate}
\item $\int x\cos x dx$
\item $\int (3x+2)\sin x dx$
\item $\int x^2\cos 2x dx$
\item $\int (5x+3)e^x dx$
\item $\int \frac{6x}{e^x} dx$
\item $\int (x^2+2x+3)e^{4x} dx$
\item $\int x\ln x dx$
\item $\int \frac{\ln x}{x^2} dx$
\item $\int \ln x dx$
\item $\int arctg x dx$
\item $\int arcsin x dx$
\end{enumerate}
\item Határozza meg az alábbi integrálokat:
\begin{enumerate}
\item $\int \frac{6}{x+3} dx$
\item $\int \frac{8}{3x-2} dx$
\item $\int \frac{10}{4-5x} dx$
\item $\int \frac{5x+2}{x-2} dx$
\item $\int \frac{x^2+3x-1}{x-1} dx$
\item $\int \frac{2x^3+4x^2+3x-7}{x-1} dx$
\item $\int \frac{3}{1+16x^2} dx$
\item $\int \frac{1}{x^2+2x+2} dx$
\item $\int \frac{6}{4x^2+4x+2} dx$
\item $\int \frac{16x+5}{1+4x^2} dx$
\item $\int \frac{6x-4}{x^2-2x+2} dx$
\item $\int \frac{36x+28}{9x^2+6x+2} dx$
\item $\int \frac{28x^3+48x^2-12x+47}{1+4x^2} dx$
\item $\int \frac{8}{x^2-4} dx$
\item $\int \frac{9}{x^2+x-6} dx$
\item $\int \frac{7}{x^2+2x-3} dx$
\item $\int \frac{14x-2}{x^2-x-12} dx$
\item $\int \frac{3x^2-5x+9}{x^2+3x-4} dx$
\item $\int \frac{5x^3+6x^2-7x+9}{x^2+6x+8} dx$
\end{enumerate}
\end{enumerate}


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