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∫ X E X D X - Mathematics

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Sum
\[\int x e^x \text{ dx }\]
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Solution

\[\int x e^x \text{ dx }\]
` "Taking x as the first function and e"^x "  as the second function"`

\[ = x\int e^x dx - \int\left\{ \frac{d}{dx}\left( x \right)\int e^x dx \right\}dx\]
\[ = x e^x - \int1\left( e^x \right)dx\]
\[ = x e^x - e^x + C\]
\[ = \left( x - 1 \right) e^x + C\]

Concept: Indefinite Integral Problems
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APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
Exercise 19.25 | Q 4 | Page 133

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