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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
If ∫g(x)dx=g(x)\int g(x) d x=g(x), then the value of the integral ∫f(x)g(x){f(x)+2f′(x)}dx\int f(x) g(x)\left\{f(x)+2 f^{\prime}(x)\right\} d x, is
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Correct option: B
{f(x)}2g(x)+C\{f(x)\}^2 g(x)+C
The correct answer is B ({f(x)}2g(x)+C\{f(x)\}^2 g(x)+C) because it results from integrating by parts and using the given condition ∫g(x)dx=g(x)\int g(x) dx = g(x).

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