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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
∫f′(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 \,\,[\,\log \,\,f\left( x \right)\,]\,\, + \,\,c
Option C is correct because the integral is solved by recognizing the form and applying a logarithmic substitution.

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