Question

\[\int e^x \left\{ f\left( x \right) + f'\left( x \right) \right\} dx =\]

 

Options

• e^x f (x) + C

• e^x + f (x)

•  2e^x f (x)

•  e^x − f (x)

Answer 1

e^x f (x) + C

 

\[\text{Let }I = \int e^x \left\{ f\left( x \right) + f'\left( x \right) \right\}dx\]

\[\text{Putting }e^x f\left( x \right) = t\]

\[ \Rightarrow \left[ e^x \cdot f\left( x \right) + e^x f'\left( x \right) \right]dx = dt\]

\[ \therefore I = \int dt\]

\[ = t + C\]

\[ = e^x f\left( x \right) + C .............\left[ \because t = e^x f\left( x \right) \right]\]