N integrate integration rules integration rule specification

NIntegrate[1 / Sqrt[x], {x, 0, 1}, Method -> {"GlobalAdaptive", Method -> "ClenshawCurtisRule"}]//InputForm

InputForm[2.]

NIntegrate[1 / Sqrt[x], {x, 0, 1}, Method -> {"LocalAdaptive", Method -> "ClenshawCurtisRule"}]//InputForm

InputForm[2.]

NIntegrate[1 / Sqrt[x], {x, 0, 1}, Method -> "LobattoKronrodRule"]//InputForm

InputForm[NIntegrate[1/Sqrt[x], {x, 0, 1}, Method -> LobattoKronrodRule]]

NIntegrate[1 / Sqrt[x], {x, 0, 1}, Method -> {"GlobalAdaptive", Method -> "LobattoKronrodRule"}]//InputForm

InputForm[2.]

NIntegrate[1 / Sqrt[x], {x, 0, 1}, Method -> "MonteCarloRule"]//InputForm

InputForm[NIntegrate[1/Sqrt[x], {x, 0, 1}, Method -> MonteCarloRule]]

NIntegrate[1 / Sqrt[x], {x, 0, 1}, Method -> {"AdaptiveMonteCarlo", Method -> "MonteCarloRule"}]//InputForm

InputForm[2.]