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Question

Assertion :∫x5/2√1+x7dx is equal to 27log∣∣x7/2+√1+x7∣∣+C Reason: ∫dx√1+x2=log∣∣x+√1+x2∣∣+C

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Both Assertion and Reason are incorrect
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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion∫x5/2√1+x7dx=∫x5/2√1+(x7/2)2dxPutting x7/2=t⇒72x5/2dx=dt∴I=27∫dt√1+t2 =27log∣∣t+√1+t2∣∣+C (∵∫dx√1+x2=log∣∣x+√1+x2∣∣+C)=27log∣∣ ∣ ∣∣x72+√1+x7∣∣ ∣ ∣∣+C∴ Reason (R) is the correct explanation for Assertion (A).

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