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$\int (x + 1)^{3 / 2} [\sin^{- 1} (\log x) + \cos^{- 1} (\log x)] dx$ is equal to

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2π5(x+1)5/2+C

π5(x+1)5/2+C

does not exist

None of these

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detailed solution

Correct option is C

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

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$\int (x + 1)^{3 / 2} [\sin^{- 1} (\log x) + \cos^{- 1} (\log x)] dx$ is equal to