If $$y=$$∫$$x2x3$$ $$1log$$⁡tdt (where$$ x>$$0$$ $$), then find dydx

Correct option is 1x(x−1)(log⁡x)−1

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$If y = \int_{x^{2}}^{x^{3}} \frac{1}{\log t} d t (where x > 0), then find \frac{d y}{d x}$

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detailed solution

Correct option is A

y=∫x2x3 1log⁡tdt∴ dydx=ddxx31log⁡x3−ddxx21log⁡x2=3x23log⁡x−2x2log⁡x=x(x−1)(log⁡x)−1

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If y=∫x2x3 1log⁡tdt (where x>0 ), then find dydx

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$If y = \int_{x^{2}}^{x^{3}} \frac{1}{\log t} d t (where x > 0), then find \frac{d y}{d x}$