biot-savart infinite wire
Because it is an infinite wire use the BS formulation of finite straight wire to the case of infinite wire. Here because the wire is along the x-axis, the x-ordinate (1) is of no importance, as any x-ordinate is identical w.r.t. infinite wire.
The distance of the field point from the wire is R = (2^2 + 3^2)^0.5 = √13.
The formula to be used (which you can verify) is
H = (i/4ΠR)(cos α + cos β) where α, β are the angles the field point makes at the end points of the wire, which are obviously Π/2 both. Therefore the Hfield is
H = i/2ΠR.
You can use Ampere's law directly in this case too, which also gives the same result.