Answer
$\sqrt {26}-\sqrt 5\approx2.863$
Work Step by Step
$\int_{2}^{5} \frac{x\cdot dx}{\sqrt {1+x^2}}=[\sqrt {1+x^2}]_{2}^{5}=[\sqrt {1+5^2}]-[\sqrt {1+2^2}]=\sqrt {26}-\sqrt 5\approx2.863$
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