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\begin{document}

\begin{center}
  \Large{12. Gyak. \\
  Helyettesítés}
\end{center}

\begin{multicols}{2}
\begin{enumerate}

 \item 
  \begin{enumerate}
   \item $\int (x-3)\sqrt[5]{x+1}$
   \item $\int \frac{1}{1+\sqrt[3]{x+1}}$
   \item $\int \frac{1}{\sqrt{x}+\sqrt[4]{x}}$
   \item $\int \frac{e^{\sqrt{x}}}{\sqrt{x}}$
   \item * $\int \frac{\sqrt{x}}{x(1+x)}$
   \item * $\int \frac{x^{\frac23}}{\sqrt[4]{x^3}+1}$
  \end{enumerate}

  \item
   \begin{enumerate}
    \item $\int \frac{e^{2x}}{e^x+1}$
	\item $\int \frac{e^{-2x}}{e^{-2x}+3}$
	\item $\int \frac{e^{3x}+4}{e^{6x}+e^{3x}}$
	\item $\int \frac{1}{e^x+e^{-x}}$
	\item $\int \frac{1}{\cosh x+1}$
   \end{enumerate}
  
  \item
   \begin{enumerate}
    \item $\int \sqrt{3x^2-3x+1}$
    \item $\int \sqrt{15+2x-x^2}$
	\item $\int \sqrt{5-2x+x^2}$
	\item $\int \frac{1}{\sqrt{\left(1-x^2\right)^3}}$
	\item $\int \frac{x^2}{\sqrt{x^2-1}}$
	\item $\int \sqrt{4x^2+4x}$
	\item $\int \sqrt{16-x^2}\cdot x^2$
	\item $\int \frac{1}{x\sqrt{9-x^2}}$
	\item $\int \sqrt{3-2x-x^2}$
   \end{enumerate}
  
  \item
   \begin{enumerate}
    \item $\int \frac{1}{\sin x+\cos x}$
	\item $\int \frac{1}{2\sin x+\cos x+1}$
	\item $\int \frac{2}{5\cos x+1}$
	\item $\int \frac{1}{5-3\cos x}$
	\item $\int \frac{1+\sin x}{\sin x(1+\cos x)}$
	\item $\int \frac{1}{\sin x \cdot \cos 2x}$
	\item $\int \frac{\cos x}{\cos x+2\sin x}$
   \end{enumerate}
  
  \item * $\int \frac{x^4}{x+\sqrt{x^2-1}}$
 \end{enumerate}
 \end{multicols}
 \end{document}
