Section+7.2+Integration+By+Parts+-+Homework

=Evaluate the integral using integration by parts.=

math \displaystyle \textbf{1)} \large \begin{equation} \int x\ e^{2x}\ dx \end{equation} math media type="custom" key="25927310"

math \displaystyle \textbf{2)} \large \begin{equation} \int x\ \sec^{2} x\ dx \end{equation} math

=Evaluate the integral.= math \displaystyle \textbf{3)} \large \begin{equation} \int x\ e^{-2x}\ dx \end{equation} math

math \displaystyle \textbf{4)} \large \begin{equation} \int x^{2}\ e^{x^{3}}\ dx \end{equation} math

math \displaystyle \textbf{5)} \large \begin{equation} \int x\ \cos\ x dx \end{equation} math

=Solve the differential equation.= math \displaystyle \textbf{6)} \large \begin{equation} \ y'\ =\ x\ e^{x^{2}} \end{equation} math

=Evaluate the integral.= math \displaystyle \textbf{7)} \large \begin{equation} \int _{0}^{\pi/2}\ x\ \cos\ x\ dx \end{equation} math

math \displaystyle \textbf{8)} \large \begin{equation} \int _{0}^{1}\ e^x\ \sin\ x\ dx \end{equation} math

math \displaystyle \textbf{9)} \large \begin{equation} \int _{1}^{2}\ x^2\ \ln\ x\ dx \end{equation} math