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\center{\Large 12. MATEMATIKA A1 FELADATSOR}

\begin{enumerate}
\item Határozza meg az alábbi integrálokat:
\begin{enumerate}
\item $\int \cos^2x dx$
\item $\int \sin^23x dx$
\item $\int \sin x \cos 2x dx$
\item $\int \sin x \sin 2x dx$
\item $\int \cos 2x \cos 3x dx$
\item $\int \sin^3x dx$
\item $\int \cos ^3x dx$
\item $\int \sin^4x dx$
\item $\int \sin^2x\cos 3x dx$
\item $\int \cos^24x \sin x dx$
\item $\int \cos^23x \sin ^22x  dx$
\end{enumerate}
\item Határozza meg az alábbi integrálokat helyettesítéssel:
\begin{enumerate}
\item $\int e^x\sin(e^x) dx$, $t=e^x$
\item $\int e^{2x}\cos(e^x) dx$, $t=e^x$
\item $\int \frac{e^{2x}}{1+e^x} dx$, $t=e^x$
\item $\int \frac{e^x}{1+e^{2x}} dx$, $t=e^x$
\item $\int \frac{1}{e^x-1} dx$, $t=e^x$
\item $\int \frac{e^x}{e^{2x}-1} dx$, $t=e^x$
\item $\int \frac{\sin \sqrt{x}}{\sqrt{x}} dx$, $t=\sqrt{x}$
\item $\int \cos \sqrt{2x} dx$, $t=\sqrt{x}$
\item $\int \frac{1}{2x-1-\sqrt{2x-1}} dx$, $t=\sqrt{2x-1}$
\item $\int \frac{6}{1+\sqrt[3]{x}} dx$, $t=\sqrt[3]{x}$
\item $\int e^{\sqrt{x}} dx$, $t=\sqrt{x}$
\item $\int x\sqrt{3x-2} dx$, $t=\sqrt{3x-2}$
\item $\int x^2\sqrt{x-1}$, $t=\sqrt{x-1}$
\end{enumerate}
\end{enumerate}


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