The correct option is D 343
∵√x+(√x−1)=√√(x−1)2+12+2√(x−1)=√(x−1)+1
And √x−2√(x−1)=(√√(x−1)2+12+2√x−1)=|√(x−1)−1|
Then ∫51√x+2√x−1+√x−2√(x−1)dx=∫51(√(x−1)+1)dx+∫51|√(x−1)−1|dx=∫51(√(x−1)+1)dx+∫21(1−√(x−1))dx+∫52(√(x−1)−1)dx==∫40(√x+1)dx=∫10(1−√x)dx+∫41(√x−1)dx=[23(x32)+x]40+[x−23x32]+[23x32−1]=323