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∫ ( X + 1 ) E X Sin 2 ( X E X ) D X - Mathematics

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Sum
\[\int\frac{\left( x + 1 \right) e^x}{\sin^2 \left( \text{x e}^x \right)} dx\]
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Solution

\[\int\frac{\left( x + 1 \right) e^x}{\sin^2 \left( \text{x e}^x \right)}dx\]
\[\text{Let x e}^x = t\]
\[ \Rightarrow \left( 1 \cdot e^x + \text{x e}^x \right) = \frac{dt}{dx}\]
\[ \Rightarrow \left( x + 1 \right) \text{e}^x dx = dt\]
\[Now, \int\frac{\left( x + 1 \right) e^x}{\sin^2 \left( \text{x e}^x \right)}dx\]
\[ = \int\frac{dt}{\sin^2 t}\]
\[ = \int {cosec}^2 \text{t dt} \]
\[ = - \text{cot} \left( t \right) + C\]
\[ = - \text{cot} \left( \text{x e}^x \right) + C\]

Concept: Indefinite Integral Problems
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APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
Exercise 19.9 | Q 48 | Page 59

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