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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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∫fβ€²(x)f(x)  log⁑  [f(x)]  dx\int \frac{{f'\left( x \right)}}{{f\left( x \right)\,\,\log \,\,\left[ {f\left( x \right)} \right]}}\,\,dx is equal to
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Correct option: C
log⁑  [log⁑  f(x)]  +  c\log \,\,\left[ {\log \,\,f\left( x \right)} \right]\,\, + \,\,c
Option C (log[log f(x)] + c) is correct because it is the result of applying u-substitution twice, first with u = log(f(x)) and then with v = log(u).

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