Problems on Techniques of Integration

Use the Integration by Parts. Set

u &=&x\\
dv &=& \cos(x)dx\;.


du &=&dx\\
v &=& \sin(x)\;.


\begin{displaymath}\int x \cos(x) dx = x \sin(x) - \int sin(x) dx \end{displaymath}


\begin{displaymath}\int x \cos(x) dx = x \sin(x) - [-\cos(x)] + C = x \sin(x) + \cos(x) + C\;.\end{displaymath}

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