∫1/x√(2x-1)dx

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∫1/x√(2x-1)dx∫1/x√(2x-1)dx∫1/x√(2x-1)dx∫dx/[x√(2x-1)]letx=(1/2)(secy)^2dx=(secy)^2.(tany)dy∫dx/[x√(2

∫1/x√(2x-1)dx
∫1/x√(2x-1)dx

∫1/x√(2x-1)dx
∫dx/[x√(2x-1)]
let
x= (1/2) (secy)^2
dx = (secy)^2.(tany) dy
∫dx/[x√(2x-1)]
=2∫ dy
=2y + C
=2arccos (1/√(2x)) + C