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Q.

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

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a

x(x−1)(log⁡x)−1

b

(x−1)(log⁡x)−1

c

x(x−1)(log⁡x)

d

x(log⁡x)−1

answer is A.

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Detailed Solution

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