Problems on Techniques of Integration

Use the Integration by Parts. Set

u &=&x\\
dv &=& e^{x}dx\;.


du &=&dx\\
v &=& e^{x}\;.


\begin{displaymath}\int x e^{x} dx = x e^{x} - \int e^{x} dx \end{displaymath}


\begin{displaymath}\int x e^{x} dx = x e^x - e^{x} + C = (x-1)e^x + C\;.\end{displaymath}

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