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Write a Value of ∫ E a X { a F ( X ) + F ′ ( X ) } D X - Mathematics

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Sum

Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .

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Solution

\[\text{ Let I }= \int e^{ax} \left[ a f\left( x \right) + f'\left( x \right) \right]dx\]
\[\text{ Let e}^{ax} . f\left( x \right) = t\]
\[ \Rightarrow \left[ e^{ax} . a f\left( x \right) + e^{ax} . f'\left( x \right) \right]dx = dt\]
\[ \therefore I = \int dt\]
\[ = t + C\]
\[ = e^{ax} . f\left( x \right) + C \left( \because t = e^{ax} . f\left( x \right) \right)\]
Concept: Methods of Integration: Integration by Substitution
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APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
Very Short Answers | Q 34 | Page 198
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