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Value of $\int_{1}^{5} {\sqrt{x + 2 \sqrt{x - 1}} + \sqrt{x - 2 (x - 1)}} dx$ is

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Correct option is D

x+(2x−1)=|x−1+1|⇒x−2x−1=|x−1−1|I=∫12 2dx+∫25 2x−1dx=2⋅1+2⋅(x−1)3/2⋅2325=2+283=343

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Value of ∫15 {x+2x−1+x−2(x−1)}dx is

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Value of $\int_{1}^{5} {\sqrt{x + 2 \sqrt{x - 1}} + \sqrt{x - 2 (x - 1)}} dx$ is