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Question
\[\int x e^x \text{ dx }\]
Sum
Solution
\[\int x e^x \text{ dx }\]
` "Taking x as the first function and e"^x " as the second function"`
\[ = x\int e^x dx - \int\left\{ \frac{d}{dx}\left( x \right)\int e^x dx \right\}dx\]
\[ = x e^x - \int1\left( e^x \right)dx\]
\[ = x e^x - e^x + C\]
\[ = \left( x - 1 \right) e^x + C\]
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