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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
Let ∫  ex  (f  (x)−f′(x))  dx=ϕ  (x)\int \,\,{e^x}\,\,\left( {f\,\,\left( x \right) - f'\left( x \right)} \right)\,\,dx = \phi \,\,\left( x \right)

Then, ∫  ex f(x)  dx\int \,\,{e^x}\,f\left( x \right)\,\,dx is equal to
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Correct option: C
12  [ϕ(x)  +  exf  (x)]\frac{1}{2}\,\,\left[ {\phi \left( x \right)\,\, + \,\,{e^x}f\,\,\left( x \right)} \right]
Option C (12 [ϕ(x) + exf  (x)]\frac{1}{2}\,\left[ {\phi \left( x \right)\, + \,{e^x}f\,\,\left( x \right)} \right]) is correct because it is derived from integration by parts and the given equation.

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