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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
If ∫g  (x)  dx=g(x)\int g\,\,\left( x \right)\,\,dx = g\left( x \right), then ∫g  (x)  {f(x)  +  f′(x)}dx\int g\,\,\left( x \right)\,\,\left\{ {f\left( x \right)\,\, + \,\,f'\left( x \right)} \right\}dx is equal to
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Correct option: C
g  (x)  f(x)  +  Cg\,\,\left( x \right)\,\,f\left( x \right)\,\, + \,\,C
Option C (g  (x)  f(x)  +  Cg\,\,( x )\,\,f( x )\,\, + \,\,C) is correct because it is derived by using integration by parts, where the integral of g(x) is g(x) itself.

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