Simplification of this integral I have an integral $\int_0^1 \sqrt{e^{2x} + e^{-2x} + 2}$ which the solution says simplifies to $ \int_0^1 e^{-x}(e^{2x} + 1)$. I understand the simplification but what happened to the constant $\sqrt{2}$? It's been awhile since I've done any computational math stuff so maybe it's just something dumb I'm missing. Please let me know. Thanks. 

Alternatively, take $e^{-2x}$ out:
$$\int_0^1 \sqrt{e^{-2x}}\sqrt{(e^{4x}+2e^{2x}+1)}dx=\int_0^1 e^{-x}\sqrt{(e^{2x}+1)^2}dx=\int_0^1 e^{-x}(e^{2x}+1)dx.$$
