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Question
\[\int e^x \left\{ f\left( x \right) + f'\left( x \right) \right\} dx =\]
Options
ex f (x) + C
ex + f (x)
2ex f (x)
ex − f (x)
MCQ
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Solution
ex f (x) + C
\[\text{Let }I = \int e^x \left\{ f\left( x \right) + f'\left( x \right) \right\}dx\]
\[\text{Putting }e^x f\left( x \right) = t\]
\[ \Rightarrow \left[ e^x \cdot f\left( x \right) + e^x f'\left( x \right) \right]dx = dt\]
\[ \therefore I = \int dt\]
\[ = t + C\]
\[ = e^x f\left( x \right) + C .............\left[ \because t = e^x f\left( x \right) \right]\]
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