Q.

∫(x+1)3/2sin−1 ⁡(log⁡ x)+cos−1 ⁡(log⁡ x)dx is equal to

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a

2π5(x+1)5/2+C

b

π5(x+1)5/2+C

c

does not exist

d

None of these

answer is C.

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Detailed Solution

∵sin−1⁡ x and cos−1 ⁡x are defined for [−1,1] For x>e,log ⁡x>1⇒sin−1 ⁡(log ⁡x)+cos−1 ⁡(log ⁡x) is not defined.
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