∫cosx/(2+cos2x)^(0.5) dx
=
∫cosx/(2+1-2sin^2x)^(0.5) dx
=
∫dsinx/(3-2sin^2x)^(0.5)
=1/√2∫d√2sinx/(3-2sin^2x)^(0.5)
=1/√2arcsin[(√2sinx)/√3]+c
∫cosx/(2+cos2x)^(0.5) dx
=
∫cosx/(2+1-2sin^2x)^(0.5) dx
=
∫dsinx/(3-2sin^2x)^(0.5)
=1/√2∫d√2sinx/(3-2sin^2x)^(0.5)
=1/√2arcsin[(√2sinx)/√3]+c